Le problème de Cauchy pour les équations différentielles d'un fluide général

Nash, J.

doi:10.24033/bsmf.1586

Nash, J.

Bulletin de la Société Mathématique de France, Tome 90 (1962), pp. 487-497.

MR Zbl | 4 citations dans Numdam

DOI : 10.24033/bsmf.1586

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     pages = {487--497},
     publisher = {Soci\'et\'e math\'ematique de France},
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     year = {1962},
     doi = {10.24033/bsmf.1586},
     mrnumber = {26 #6590},
     zbl = {0113.19405},
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Nash, J. Le problème de Cauchy pour les équations différentielles d'un fluide général. Bulletin de la Société Mathématique de France, Tome 90 (1962), pp. 487-497. doi : 10.24033/bsmf.1586. https://www.numdam.org/articles/10.24033/bsmf.1586/

Bibliographie
Cité par

[1] Friedman (Avner). - Interior estimates for parabolic systems of partial differential equations, J. Math. and Mech., t. 7, 1958, p. 393-418. | MR | Zbl

[2] Landau (L. D.) and Lifšic (E. M.). - Fluid mechanics [Translated from Mekhanika splošnykh sred, Izdanie vtoroe. Moscou, 1954]. - London, Pergamon Press, 1959.

[3] Pogorzelski (Withold). - Propriétés des solutions du système parabolique d'équations aux dérivées partielles, Math. Scand., t. 6, 1958, p. 237-262. | Zbl

[4] Serrin (James). - The uniqueness of compressible fluid motions, Arch. for rat. Mech. and Anal.. t. 3, 1959, p. 271-288. | MR | Zbl

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Huang, Xiangdi; Yan, Wei Local weak solution of the isentropic compressible Navier–Stokes equations, Journal of Mathematical Physics, Volume 62 (2021) no. 11 | DOI:10.1063/5.0054450
Wu, Yunshun; Xiao, Li; Yu, Rongfeng Global strong solutions for viscous radiative gas with degenerate temperature dependent heat conductivity in one-dimensional unbounded domains, Journal of Mathematical Physics, Volume 62 (2021) no. 2 | DOI:10.1063/5.0039346
Song, Changzhen; Zhang, Jianwen On the compressible viscous barotropic flows subject to large external potential forces in a half space with Navier's boundary conditions, Mathematical Methods in the Applied Sciences, Volume 44 (2021) no. 5, p. 3705 | DOI:10.1002/mma.6975
Li, Hao; Li, Yachun Local well‐posedness of compressible radiation hydrodynamic equations with density‐dependent viscosities and vacuum, Mathematical Methods in the Applied Sciences, Volume 44 (2021) no. 6, p. 4715 | DOI:10.1002/mma.7064
Gao, Jincheng; Wei, Zhengzhen; Yao, Zheng-an Decay of strong solution for the compressible Navier–Stokes equations with large initial data, Nonlinear Analysis, Volume 213 (2021), p. 112494 | DOI:10.1016/j.na.2021.112494
Xiao, Li; Lu, Linzhang Global strong solution for compressible and radiative MHD flow with density-dependent viscosity and degenerate heat-conductivity in unbounded domains, Nonlinear Analysis: Real World Applications, Volume 60 (2021), p. 103312 | DOI:10.1016/j.nonrwa.2021.103312
Xu, Fuyi; Chi, Meiling The unique global solvability and optimal time decay rates for a multi-dimensional compressible generic two-fluid model with capillarity effects *, Nonlinearity, Volume 34 (2021) no. 1, p. 164 | DOI:10.1088/1361-6544/abaff0
Huang, Xiangdi On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum, Science China Mathematics, Volume 64 (2021) no. 8, p. 1771 | DOI:10.1007/s11425-019-9755-3
Li, Wei; Shang, Zhaoyang; Tang, Fuquan Global existence of classical solutions for two-dimensional isentropic compressible Navier–Stokes equations with small initial mass, Advances in Difference Equations, Volume 2020 (2020) no. 1 | DOI:10.1186/s13662-020-02675-0
Li, Jinkai; Xin, Zhouping Entropy bounded solutions to the one-dimensional compressible Navier-Stokes equations with zero heat conduction and far field vacuum, Advances in Mathematics, Volume 361 (2020), p. 106923 | DOI:10.1016/j.aim.2019.106923
Danchin, Raphaël; Fanelli, Francesco; Paicu, Marius A well-posedness result for viscous compressible fluids with only bounded density, Analysis PDE, Volume 13 (2020) no. 1, p. 275 | DOI:10.2140/apde.2020.13.275
Zhang, Zhifei; Zi, Ruizhao Convergence to equilibrium for the solution of the full compressible Navier-Stokes equations, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 37 (2020) no. 2, p. 457 | DOI:10.1016/j.anihpc.2019.09.001
Li, Jinkai Global Small Solutions of Heat Conductive Compressible Navier–Stokes Equations with Vacuum: Smallness on Scaling Invariant Quantity, Archive for Rational Mechanics and Analysis, Volume 237 (2020) no. 2, p. 899 | DOI:10.1007/s00205-020-01521-7
Yu, Haibo; Zhang, Peixin Global strong solutions to the 3D full compressible Navier–Stokes equations with density–temperature–dependent viscosities in bounded domains, Journal of Differential Equations, Volume 268 (2020) no. 12, p. 7286 | DOI:10.1016/j.jde.2019.11.065
Wen, Huanyao; Zhao, Xinhua On a simplified compressible Navier-Stokes equations with temperature-dependent viscosity, Journal of Differential Equations, Volume 268 (2020) no. 5, p. 1974 | DOI:10.1016/j.jde.2019.09.023
Huang, Bin; Shi, Xiaoding Nonlinearly exponential stability of compressible Navier-Stokes system with degenerate heat-conductivity, Journal of Differential Equations, Volume 268 (2020) no. 5, p. 2464 | DOI:10.1016/j.jde.2019.09.006
Hu, Xianpeng; Wu, Guochun Optimal decay rates of isentropic compressible Navier-Stokes equations with discontinuous initial data, Journal of Differential Equations, Volume 269 (2020) no. 10, p. 8132 | DOI:10.1016/j.jde.2020.06.021
Hu, Yuxi; Racke, Reinhard Hyperbolic compressible Navier-Stokes equations, Journal of Differential Equations, Volume 269 (2020) no. 4, p. 3196 | DOI:10.1016/j.jde.2020.02.025
Shang, Zhaoyang Global strong solutions to the two-dimensional full compressible Navier-Stokes equations with vacuum, Journal of Mathematical Analysis and Applications, Volume 481 (2020) no. 1, p. 123459 | DOI:10.1016/j.jmaa.2019.123459
Mitra, Sourav Local Existence of Strong Solutions of a Fluid–Structure Interaction Model, Journal of Mathematical Fluid Mechanics, Volume 22 (2020) no. 4 | DOI:10.1007/s00021-020-00520-8
Wang, Yongfu Weak Serrin‐type criterion for the three‐dimensional viscous compressible Navier–Stokes system, Journal of the London Mathematical Society, Volume 102 (2020) no. 1, p. 125 | DOI:10.1112/jlms.12315
Li, Kexin; Shu, Xuanlin; Xu, Xiaojing Global existence of strong solutions to compressible Navier–Stokes system with degenerate heat conductivity in unbounded domains, Mathematical Methods in the Applied Sciences, Volume 43 (2020) no. 4, p. 1543 | DOI:10.1002/mma.5969
Li, Jinkai Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D, Nonlinearity, Volume 33 (2020) no. 5, p. 2181 | DOI:10.1088/1361-6544/ab6c7b
Li, Yang; Sun, Yongzhong; Zatorska, Ewelina Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data, Nonlinearity, Volume 33 (2020) no. 8, p. 4075 | DOI:10.1088/1361-6544/ab801c
Zhai, Xiaoping; Li, Yongsheng; Zhou, Fujun Global Large Solutions to the Three Dimensional Compressible Navier–Stokes Equations, SIAM Journal on Mathematical Analysis, Volume 52 (2020) no. 2, p. 1806 | DOI:10.1137/19m1265843
Li, Yang; Jiang, Lingyu Global Weak Solutions for the Cauchy Problem to One-Dimensional Heat-Conductive MHD Equations of Viscous Non-resistive Gas, Acta Applicandae Mathematicae, Volume 163 (2019) no. 1, p. 185 | DOI:10.1007/s10440-018-0219-5
Li, Jing; Xin, Zhouping Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier–Stokes Equations with Vacuum, Annals of PDE, Volume 5 (2019) no. 1 | DOI:10.1007/s40818-019-0064-5
Li, Hai-Liang; Wang, Yuexun; Xin, Zhouping Non-existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier–Stokes Equations, Archive for Rational Mechanics and Analysis, Volume 232 (2019) no. 2, p. 557 | DOI:10.1007/s00205-018-1328-z
Li, Yachun; Pan, Ronghua; Zhu, Shengguo On Classical Solutions for Viscous Polytropic Fluids with Degenerate Viscosities and Vacuum, Archive for Rational Mechanics and Analysis, Volume 234 (2019) no. 3, p. 1281 | DOI:10.1007/s00205-019-01412-6
Cui, Meiying; Song, Wenjing Global existence of weak solution for the compressible Navier–Stokes–Poisson system with density-dependent viscosity, Boundary Value Problems, Volume 2019 (2019) no. 1 | DOI:10.1186/s13661-019-1268-z
Li, Wei; Shang, Zhaoyang Global large solutions to the planar magnetohydrodynamics equations with constant heat conductivity, Boundary Value Problems, Volume 2019 (2019) no. 1 | DOI:10.1186/s13661-019-1275-0
Xu, Jiang A Low-Frequency Assumption for Optimal Time-Decay Estimates to the Compressible Navier–Stokes Equations, Communications in Mathematical Physics, Volume 371 (2019) no. 2, p. 525 | DOI:10.1007/s00220-019-03415-6
Zhumagulov, B.; Temirbekov, N.; Baigereyev, D.; Turarov, A. Stability Analysis of a Difference Scheme for the Dynamic Model of Gas Lift Process, Computational and Information Technologies in Science, Engineering and Education, Volume 998 (2019), p. 236 | DOI:10.1007/978-3-030-12203-4_24
Li, Yachun; Shang, Zhaoyang Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients, Journal of Hyperbolic Differential Equations, Volume 16 (2019) no. 03, p. 443 | DOI:10.1142/s0219891619500164
Li, Zilai; Ma, Yan; Ou, Yaobin Global strong solutions to 1-D vacuum free boundary problem for compressible Navier–Stokes equations with variable viscosity and thermal conductivity, Journal of Mathematical Analysis and Applications, Volume 474 (2019) no. 2, p. 1153 | DOI:10.1016/j.jmaa.2019.02.009
Chen, Zhi-Min; Zhai, Xiaoping Global Large Solutions and Incompressible Limit for the Compressible Navier–Stokes Equations, Journal of Mathematical Fluid Mechanics, Volume 21 (2019) no. 2 | DOI:10.1007/s00021-019-0428-3
Yu, Rongfeng Singularity formation of the compressible non-barotropic flows with zero heat conductivity, Journal of Mathematical Physics, Volume 60 (2019) no. 3 | DOI:10.1063/1.5085807
Ye, Yulin; Li, Zilai The large time behavior of the free boundary for one dimensional compressible Navier-Stokes equations, Journal of Mathematical Physics, Volume 60 (2019) no. 7 | DOI:10.1063/1.5082004
Chen, Jiecheng; Wan, Renhui ILL-POSEDNESS FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH THE VELOCITY IN FRAMEWORK, Journal of the Institute of Mathematics of Jussieu, Volume 18 (2019) no. 4, p. 829 | DOI:10.1017/s1474748017000238
Qin, Xulong; Yang, Tong; Yao, Zheng-an; Zhou, Wenshu Vanishing shear viscosity limit and boundary layer study for the planar MHD system, Mathematical Models and Methods in Applied Sciences, Volume 29 (2019) no. 06, p. 1139 | DOI:10.1142/s0218202519500180
Jin, Chunyin The local existence and blowup criterion for strong solutions to the kinetic Cucker–Smale model coupled with the compressible Navier–Stokes equations, Nonlinear Analysis: Real World Applications, Volume 49 (2019), p. 217 | DOI:10.1016/j.nonrwa.2019.03.007
Huang, Bin; Shi, Xiaoding; Sun, Ying Global strong solutions to magnetohydrodynamics with density-dependent viscosity and degenerate heat-conductivity, Nonlinearity, Volume 32 (2019) no. 11, p. 4395 | DOI:10.1088/1361-6544/ab3059
Yin, Haiyan Converge rates towards stationary solutions for the outflow problem of planar magnetohydrodynamics on a half line, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 149 (2019) no. 5, p. 1291 | DOI:10.1017/prm.2018.66
Lei, Zhen; Xin, Zhouping On scaling invariance and type-I singularities for the compressible Navier-Stokes equations, Science China Mathematics, Volume 62 (2019) no. 11, p. 2271 | DOI:10.1007/s11425-018-9363-1
De Lellis, Camillo The Masterpieces of John Forbes Nash Jr., The Abel Prize 2013-2017 (2019), p. 391 | DOI:10.1007/978-3-319-99028-6_19
Danchin, Raphaël; Mucha, Piotr Bogusław From compressible to incompressible inhomogeneous flows in the case of large data, Tunisian Journal of Mathematics, Volume 1 (2019) no. 1, p. 127 | DOI:10.2140/tunis.2019.1.127
Huang, Xiangdi; Li, Jing Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier–Stokes System with Vacuum and Large Oscillations, Archive for Rational Mechanics and Analysis, Volume 227 (2018) no. 3, p. 995 | DOI:10.1007/s00205-017-1188-y
Li, Lin-an; Wang, Teng; Wang, Yi Stability of Planar Rarefaction Wave to 3D Full Compressible Navier–Stokes Equations, Archive for Rational Mechanics and Analysis, Volume 230 (2018) no. 3, p. 911 | DOI:10.1007/s00205-018-1260-2
Ngo, Van-Sang; Scrobogna, Stefano Dispersive effects of weakly compressible and fast rotating inviscid fluids, Discrete Continuous Dynamical Systems - A, Volume 38 (2018) no. 2, p. 749 | DOI:10.3934/dcds.2018033
Jiang, Song; Ju, Qiangchang Symmetric Solutions to the Viscous Gas Equations, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 1711 | DOI:10.1007/978-3-319-13344-7_35
Danchin, Raphaël Fourier Analysis Methods for the Compressible Navier-Stokes Equations, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 1843 | DOI:10.1007/978-3-319-13344-7_49
Kotschote, Matthias Local and Global Existence of Strong Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Maximal Regularity, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 1905 | DOI:10.1007/978-3-319-13344-7_50
Li, Jing; Xin, Zhou Ping Global Existence of Regular Solutions with Large Oscillations and Vacuum for Compressible Flows, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 2037 | DOI:10.1007/978-3-319-13344-7_58
Huang, Xiangdi; Xin, Zhou Ping Finite Time Blow-Up of Regular Solutions for Compressible Flows, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 2183 | DOI:10.1007/978-3-319-13344-7_57
Jiang, Song; Zhou, Chunhui Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 2549 | DOI:10.1007/978-3-319-13344-7_63
Giovangigli, Vincent Solutions for Models of Chemically Reacting Compressible Mixtures, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 2979 | DOI:10.1007/978-3-319-13344-7_73
Wang, Yun; Huang, Xiangdi On center singularity for compressible spherically symmetric nematic liquid crystal flows, Journal of Differential Equations, Volume 264 (2018) no. 8, p. 5197 | DOI:10.1016/j.jde.2017.12.035
Li, Yang Global well-posedness to the one-dimensional model for planar non-resistive magnetohydrodynamics with large data and vacuum, Journal of Mathematical Analysis and Applications, Volume 462 (2018) no. 2, p. 1342 | DOI:10.1016/j.jmaa.2018.02.047
Feng, Yue-Hong; Liu, Cun-Ming Stability of steady-state solutions to Navier–Stokes–Poisson systems, Journal of Mathematical Analysis and Applications, Volume 462 (2018) no. 2, p. 1679 | DOI:10.1016/j.jmaa.2018.03.001
Yin, Haiyan Stability of stationary solutions for inflow problem on the planar magnetohydrodynamics, Journal of Mathematical Physics, Volume 59 (2018) no. 2 | DOI:10.1063/1.5023583
Bae, H‐O.; Zajączkowski, Wojciech M. Global regular motions for compressible barotropic viscous fluids: Stability, Mathematical Methods in the Applied Sciences, Volume 41 (2018) no. 15, p. 5869 | DOI:10.1002/mma.4860
Guo, Zhenhua; Wang, Mei; Wang, Yi Global solution to 3D spherically symmetric compressible Navier–Stokes equations with large data, Nonlinear Analysis: Real World Applications, Volume 40 (2018), p. 260 | DOI:10.1016/j.nonrwa.2017.09.004
Si, Xin; Zhang, Jianwen; Zhao, Junning Global classical solutions of compressible isentropic Navier–Stokes equations with small density, Nonlinear Analysis: Real World Applications, Volume 42 (2018), p. 53 | DOI:10.1016/j.nonrwa.2017.12.005
Yin, Haiyan Stability of composite wave for inflow problem on the planar magnetohydrodynamics, Nonlinear Analysis: Real World Applications, Volume 44 (2018), p. 305 | DOI:10.1016/j.nonrwa.2018.05.008
Liang, Zhilei; Shuai, Jiangyu Global strong solution for the full MHD equations with vacuum and large data, Nonlinear Analysis: Real World Applications, Volume 44 (2018), p. 385 | DOI:10.1016/j.nonrwa.2018.05.012
Jiu, Quansen; Wang, Yi; Xin, Zhouping Global classical solution to two-dimensional compressible Navier–Stokes equations with large data inR2, Physica D: Nonlinear Phenomena, Volume 376-377 (2018), p. 180 | DOI:10.1016/j.physd.2017.12.006
Fang, Daoyuan; Zhang, Ting; Zi, Ruizhao Global Solutions to the Isentropic Compressible Navier–Stokes Equations with a Class of Large Initial Data, SIAM Journal on Mathematical Analysis, Volume 50 (2018) no. 5, p. 4983 | DOI:10.1137/17m1122062
Yang, Jiayan; Liu, Ruikuan The existence results for a new 2‐D compressible fluid model with the horizontal thermal gradient effect, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 98 (2018) no. 8, p. 1302 | DOI:10.1002/zamm.201700176
Li, Yang Global strong solutions to the one-dimensional heat-conductive model for planar non-resistive magnetohydrodynamics with large data, Zeitschrift für angewandte Mathematik und Physik, Volume 69 (2018) no. 3 | DOI:10.1007/s00033-018-0970-5
Tani, Atusi, Volume 1903 (2017), p. 020003 | DOI:10.1063/1.5012614
Wang, Mei; Li, Zilai; Guo, Zhenhua Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary, Communications on Pure Applied Analysis, Volume 16 (2017) no. 1, p. 1 | DOI:10.3934/cpaa.2017001
Shibata, Yoshihiro; Enomoto, Yuko Global Existence of Classical Solutions and Optimal Decay Rate Via the Theory of Semigroup, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2017), p. 1 | DOI:10.1007/978-3-319-10151-4_52-1
Jiang, Song; Zhou, Chunhui Existence of Stationary Weak Solutions for the Isentropic and Isothermal Flows, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2017), p. 1 | DOI:10.1007/978-3-319-10151-4_63-1
Kotschote, Matthias Local and Global Existence of Strong Solutions Near General Equilibria, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2017), p. 1 | DOI:10.1007/978-3-319-10151-4_50-1
Huang, Xiangdi Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier–Stokes equations, Journal of Differential Equations, Volume 262 (2017) no. 3, p. 1341 | DOI:10.1016/j.jde.2016.10.013
Duan, Ran; Guo, Ai; Zhu, Changjiang Global strong solution to compressible Navier–Stokes equations with density dependent viscosity and temperature dependent heat conductivity, Journal of Differential Equations, Volume 262 (2017) no. 8, p. 4314 | DOI:10.1016/j.jde.2017.01.007
Li, Yachun; Pan, Ronghua; Zhu, Shengguo On Classical Solutions to 2D Shallow Water Equations with Degenerate Viscosities, Journal of Mathematical Fluid Mechanics, Volume 19 (2017) no. 1, p. 151 | DOI:10.1007/s00021-016-0276-3
Hu, Yuxi; Racke, Reinhard Compressible Navier–Stokes Equations with Revised Maxwell’s Law, Journal of Mathematical Fluid Mechanics, Volume 19 (2017) no. 1, p. 77 | DOI:10.1007/s00021-016-0266-5
Yin, Haiyan The stability of contact discontinuity for compressible planar magnetohydrodynamics, Kinetic Related Models, Volume 10 (2017) no. 4, p. 1235 | DOI:10.3934/krm.2017047
KONG, Huihui; LI, Hai-Liang; ZHANG, Xingwei A blow-up criterion of spherically symmetric strong solutions to 3d compressible navier-stokes equations with free boundary, Acta Mathematica Scientia, Volume 36 (2016) no. 4, p. 1153 | DOI:10.1016/s0252-9602(16)30060-1
Bian, Dongfen; Yuan, Baoquan Local well-posedness in critical spaces for the compressible MHD equations, Applicable Analysis, Volume 95 (2016) no. 2, p. 239 | DOI:10.1080/00036811.2014.910651
Huang, Xiangdi; Xin, Zhouping On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity, Discrete and Continuous Dynamical Systems, Volume 36 (2016) no. 8, p. 4477 | DOI:10.3934/dcds.2016.36.4477
Huang, Xiangdi; Xin, Zhou Ping Finite Time Blowup of Regular Solutions, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_57-1
LI, Jing; XIN, Zhouping Global Existence of Regular Solutions with Large Oscillations and Vacuum, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_58-1
Jiang, Song; Ju, Qiangchang Symmetric Solutions to the Viscous Gas Equations, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_35-1
Danchin, Raphaël Fourier Analysis Methods for the Compressible Navier-Stokes Equations, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_49-1
Giovangigli, Vincent Solutions for Models of Chemically Reacting Mixtures, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_73-1
Sun, Yongzhong; Zhang, Zhifei Blow-Up Criteria of Strong Solutions and Conditional Regularity of Weak Solutions, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_54-1
Huang, Xiangdi; Li, Jing Existence and blowup behavior of global strong solutions to the two-dimensional barotrpic compressible Navier–Stokes system with vacuum and large initial data, Journal de Mathématiques Pures et Appliquées, Volume 106 (2016) no. 1, p. 123 | DOI:10.1016/j.matpur.2016.02.003
Hu, Yuxi; Racke, Reinhard Compressible Navier–Stokes Equations with hyperbolic heat conduction, Journal of Hyperbolic Differential Equations, Volume 13 (2016) no. 02, p. 233 | DOI:10.1142/s0219891616500077
Wan, Ling; Wang, Tao Large-time behavior of solutions to the equations of a viscous heat-conducting flow with shear viscosity in unbounded domains, Journal of Mathematical Analysis and Applications, Volume 436 (2016) no. 1, p. 366 | DOI:10.1016/j.jmaa.2015.11.062
Cai, Xiaoyun; Sun, Yongzhong Blowup criteria for strong solutions to the compressible Navier–Stokes equations with variable viscosity, Nonlinear Analysis: Real World Applications, Volume 29 (2016), p. 1 | DOI:10.1016/j.nonrwa.2015.10.007
Fang, Li; Guo, Zhenhua Global well-posedness of strong solutions to the two-dimensional barotropic compressible Navier–Stokes equations with vacuum, Zeitschrift für angewandte Mathematik und Physik, Volume 67 (2016) no. 2 | DOI:10.1007/s00033-016-0619-1
LU, Yunguang; KLINGENBERG, Christian; KOLEY, Ujjwal; LU, Xuezhou Decay rate for degenerate convection diffusion equations in both one and several space dimensions, Acta Mathematica Scientia, Volume 35 (2015) no. 2, p. 281 | DOI:10.1016/s0252-9602(15)60001-7
Zhao, Junning; Zhang, Jianwen; Zhang, Peixin On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 2, p. 1085 | DOI:10.3934/dcds.2016.36.1085
Paddick, Matthew The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 5, p. 2673 | DOI:10.3934/dcds.2016.36.2673
Chikami, Noboru; Danchin, Raphaël On the well-posedness of the full compressible Navier–Stokes system in critical Besov spaces, Journal of Differential Equations, Volume 258 (2015) no. 10, p. 3435 | DOI:10.1016/j.jde.2015.01.012
Zhu, Shengguo Existence results for viscous polytropic fluids with degenerate viscosity coefficients and vacuum, Journal of Differential Equations, Volume 259 (2015) no. 1, p. 84 | DOI:10.1016/j.jde.2015.01.048
Qian, Jinju; Zhao, Junning Global existence of classical solutions for isentropic compressible Navier–Stokes equations with small initial density, Journal of Differential Equations, Volume 259 (2015) no. 11, p. 6830 | DOI:10.1016/j.jde.2015.08.007
Li, Zilai; Guo, Zhenhua Global existence of weak solution to the free boundary problem for compressible Navier-Stokes, Kinetic and Related Models, Volume 9 (2015) no. 1, p. 75 | DOI:10.3934/krm.2016.9.75
Huang, Xiangdi On formation of singularity of spherically symmetric nonbarotropic flows, Kyoto Journal of Mathematics, Volume 55 (2015) no. 1 | DOI:10.1215/21562261-2801813
Hu, Yuxi On initial boundary value problems for planar magnetohydrodynamics with large data, Mathematical Methods in the Applied Sciences, Volume 38 (2015) no. 17, p. 4111 | DOI:10.1002/mma.3351
Zhang, Peixin Global classical solution to the 3D isentropic compressible Navier-Stokes equations with general initial data and a density-dependent viscosity coefficient, Mathematical Methods in the Applied Sciences, Volume 38 (2015) no. 6, p. 1158 | DOI:10.1002/mma.3137
Lai, Ning-An Blow up of classical solutions to the isentropic compressible Navier–Stokes equations, Nonlinear Analysis: Real World Applications, Volume 25 (2015), p. 112 | DOI:10.1016/j.nonrwa.2015.03.005
Lv, Boqiang; Huang, Bin On strong solutions to the Cauchy problem of the two-dimensional compressible magnetohydrodynamic equations with vacuum, Nonlinearity, Volume 28 (2015) no. 2, p. 509 | DOI:10.1088/0951-7715/28/2/509
Hu, Yuxi On global solutions and asymptotic behavior of planar magnetohydrodynamics with large data, Quarterly of Applied Mathematics, Volume 73 (2015) no. 4, p. 759 | DOI:10.1090/qam/1413
Li, Jing; Zhang, Jianwen; Zhao, Junning On the Global Motion of Viscous Compressible Barotropic Flows Subject to Large External Potential Forces and Vacuum, SIAM Journal on Mathematical Analysis, Volume 47 (2015) no. 2, p. 1121 | DOI:10.1137/130941298
Hu, Yuxi; Ju, Qiangchang Global large solutions of magnetohydrodynamics with temperature-dependent heat conductivity, Zeitschrift für angewandte Mathematik und Physik, Volume 66 (2015) no. 3, p. 865 | DOI:10.1007/s00033-014-0446-1
YE, Yulin; DOU, Changsheng; JIU, Quansen Local well-posedness to the cauchy problem of the 3-D compressible navier-stokes equations with density-dependent viscosity, Acta Mathematica Scientia, Volume 34 (2014) no. 3, p. 851 | DOI:10.1016/s0252-9602(14)60055-2
Wang, Yongfu; Zhang, Qin Blowup analysis for two-dimensional viscous compressible, heat-conductive Navier–Stokes equations, Applied Mathematics and Computation, Volume 232 (2014), p. 719 | DOI:10.1016/j.amc.2014.01.103
Perepelitsa, Misha Weak Solutions of the Navier–Stokes Equations for Compressible Flows in a Half-Space with No-Slip Boundary Conditions, Archive for Rational Mechanics and Analysis, Volume 212 (2014) no. 3, p. 709 | DOI:10.1007/s00205-014-0727-z
Wang, Chao; Wang, Wei; Zhang, Zhifei Global Well-Posedness of Compressible Navier–Stokes Equations for Some Classes of Large Initial Data, Archive for Rational Mechanics and Analysis, Volume 213 (2014) no. 1, p. 171 | DOI:10.1007/s00205-014-0735-z
Kotschote, Matthias Dynamical Stability of Non-Constant Equilibria for the Compressible Navier–Stokes Equations in Eulerian Coordinates, Communications in Mathematical Physics, Volume 328 (2014) no. 2, p. 809 | DOI:10.1007/s00220-014-2023-z
Li, Jing; Liang, Zhilei On local classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier–Stokes equations with vacuum, Journal de Mathématiques Pures et Appliquées, Volume 102 (2014) no. 4, p. 640 | DOI:10.1016/j.matpur.2014.02.001
Jiu, Quansen; Wang, Yi; Xin, Zhouping Global Well-Posedness of 2D Compressible Navier–Stokes Equations with Large Data and Vacuum, Journal of Mathematical Fluid Mechanics, Volume 16 (2014) no. 3, p. 483 | DOI:10.1007/s00021-014-0171-8
Dou, Changsheng; Jiu, Quansen Remark on stability of rarefaction waves to the one‐dimensional compressible Navier–Stokes equations with density‐dependent viscosity coefficient, Mathematical Methods in the Applied Sciences, Volume 37 (2014) no. 1, p. 32 | DOI:10.1002/mma.2781
Suen, Anthony Global existence of weak solution to Navier–Stokes equations with large external force and general pressure, Mathematical Methods in the Applied Sciences, Volume 37 (2014) no. 17, p. 2716 | DOI:10.1002/mma.3012
Luo, Zhen Global existence of classical solutions to two‐dimensional Navier–Stokes equations with Cauchy data containing vacuum, Mathematical Methods in the Applied Sciences, Volume 37 (2014) no. 9, p. 1333 | DOI:10.1002/mma.2896
Wang, Yun One new blowup criterion for the 2D full compressible Navier–Stokes system, Nonlinear Analysis: Real World Applications, Volume 16 (2014), p. 214 | DOI:10.1016/j.nonrwa.2013.09.020
Feng, Yue-Hong; Peng, Yue-Jun; Wang, Shu Asymptotic behavior of global smooth solutions for full compressible Navier–Stokes–Maxwell equations, Nonlinear Analysis: Real World Applications, Volume 19 (2014), p. 105 | DOI:10.1016/j.nonrwa.2014.03.004
Łasica, Michał On steady solutions to vacuumless Newtonian models of compressible flow, Nonlinearity, Volume 27 (2014) no. 11, p. 2663 | DOI:10.1088/0951-7715/27/11/2663
Zhang, PeiXin; Zhao, JunNing Existence and uniqueness of global classical solutions to 3D isentropic compressible Navier-Stokes equations with general initial data, Science China Mathematics, Volume 57 (2014) no. 7, p. 1463 | DOI:10.1007/s11425-013-4717-7
BIAN, Dongfen; GUO, Boling Well-Posedness in Critical Spaces for the Full Compressible Mhd Equations, Acta Mathematica Scientia, Volume 33 (2013) no. 4, p. 1153 | DOI:10.1016/s0252-9602(13)60071-5
Liu, Shengquan; Zhang, Jianwen A note on the blow-up criterion for the compressible isentropic Navier–Stokes equations with vacuum, Applied Mathematics Letters, Volume 26 (2013) no. 5, p. 584 | DOI:10.1016/j.aml.2012.12.011
Huang, Xiangdi; Li, Jing; Wang, Yong Serrin-Type Blowup Criterion for Full Compressible Navier–Stokes System, Archive for Rational Mechanics and Analysis, Volume 207 (2013) no. 1, p. 303 | DOI:10.1007/s00205-012-0577-5
Xin, Zhouping; Yan, Wei On Blowup of Classical Solutions to the Compressible Navier-Stokes Equations, Communications in Mathematical Physics, Volume 321 (2013) no. 2, p. 529 | DOI:10.1007/s00220-012-1610-0
Huang, Xiangdi; Li, Jing Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows, Communications in Mathematical Physics, Volume 324 (2013) no. 1, p. 147 | DOI:10.1007/s00220-013-1791-1
Zhang, Jingjun; Zhu, Junlei Global solutions for a one-dimensional problem in conducting fluids, Communications in Nonlinear Science and Numerical Simulation, Volume 18 (2013) no. 8, p. 1989 | DOI:10.1016/j.cnsns.2012.12.008
Duan, Ben; Luo, Zhen Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations, Communications on Pure Applied Analysis, Volume 12 (2013) no. 6, p. 2543 | DOI:10.3934/cpaa.2013.12.2543
Enomoto, Yuko; Shibata, Yoshihiro On the $\mathcal{R}$-Sectoriality and the Initial Boundary Value Problem for the Viscous Compressible Fluid Flow, Funkcialaj Ekvacioj, Volume 56 (2013) no. 3, p. 441 | DOI:10.1619/fesi.56.441
Jiu, Quansen; Wang, Yi; Xin, Zhouping Global well-posedness of the Cauchy problem of two-dimensional compressible Navier–Stokes equations in weighted spaces, Journal of Differential Equations, Volume 255 (2013) no. 3, p. 351 | DOI:10.1016/j.jde.2013.04.014
Liu, Shengquan; Zhang, Jianwen; Zhao, Junning Global classical solutions for 3D compressible Navier–Stokes equations with vacuum and a density-dependent viscosity coefficient, Journal of Mathematical Analysis and Applications, Volume 401 (2013) no. 2, p. 795 | DOI:10.1016/j.jmaa.2012.12.056
Huang, Xiangdi; Wang, Yun A Serrin criterion for compressible nematic liquid crystal flows, Mathematical Methods in the Applied Sciences, Volume 36 (2013) no. 11, p. 1363 | DOI:10.1002/mma.2689
Suen, Anthony Global solutions of the Navier–Stokes equations for isentropic flow with large external potential force, Zeitschrift für angewandte Mathematik und Physik, Volume 64 (2013) no. 3, p. 767 | DOI:10.1007/s00033-012-0263-3
Peixin, Zhang; Xuemei, Deng; Junning, Zhao Global Classical Solutions to the 3-D Isentropic Compressible Navier-Stokes Equations with General Initial Energy, Acta Mathematica Scientia, Volume 32 (2012) no. 6, p. 2141 | DOI:10.1016/s0252-9602(12)60166-0
Huang, Xiangdi; Li, Jing; Xin, Zhouping Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations, Communications on Pure and Applied Mathematics, Volume 65 (2012) no. 4, p. 549 | DOI:10.1002/cpa.21382
Deng, XueMei; Zhang, PeiXin; Zhao, JunNing Global classical solution to the three-dimensional isentropic compressible Navier-Stokes equations with general initial data, Science China Mathematics, Volume 55 (2012) no. 12, p. 2457 | DOI:10.1007/s11425-012-4481-0
Haspot, Boris Existence of strong solutions in critical spaces for barotropic viscous fluids in larger spaces, Science China Mathematics, Volume 55 (2012) no. 2, p. 309 | DOI:10.1007/s11425-012-4360-8
Haspot, Boris Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids, Archive for Rational Mechanics and Analysis, Volume 202 (2011) no. 2, p. 427 | DOI:10.1007/s00205-011-0430-2
Huang, Xiangdi; Li, Jing; Xin, Zhouping Blowup Criterion for Viscous Baratropic Flows with Vacuum States, Communications in Mathematical Physics, Volume 301 (2011) no. 1, p. 23 | DOI:10.1007/s00220-010-1148-y
Dongfen Bian; Baoquan Yuan; Yue Hu, International Conference on Information Science and Technology (2011), p. 1098 | DOI:10.1109/icist.2011.5765162
Sun, Yongzhong; Wang, Chao; Zhang, Zhifei A Beale–Kato–Majda blow-up criterion for the 3-D compressible Navier–Stokes equations, Journal de Mathématiques Pures et Appliquées, Volume 95 (2011) no. 1, p. 36 | DOI:10.1016/j.matpur.2010.08.001
Li, Jing; Matsumura, Akitaka On the Navier–Stokes equations for three-dimensional compressible barotropic flow subject to large external potential forces with discontinuous initial data, Journal de Mathématiques Pures et Appliquées, Volume 95 (2011) no. 5, p. 495 | DOI:10.1016/j.matpur.2010.12.002
Haspot, Boris Well-posedness in critical spaces for the system of compressible Navier–Stokes in larger spaces, Journal of Differential Equations, Volume 251 (2011) no. 8, p. 2262 | DOI:10.1016/j.jde.2011.06.013
Germain, Pierre Weak–Strong Uniqueness for the Isentropic Compressible Navier–Stokes System, Journal of Mathematical Fluid Mechanics, Volume 13 (2011) no. 1, p. 137 | DOI:10.1007/s00021-009-0006-1
Wang, Changjia; Yuan, Hongjun Global strong solutions for a class of compressible non-Newtonian fluids with vacuum, Mathematical Methods in the Applied Sciences, Volume 34 (2011) no. 4, p. 397 | DOI:10.1002/mma.1364
Dias, João Paulo; Frid, Hermano Short Wave–Long Wave Interactions for Compressible Navier–Stokes Equations, SIAM Journal on Mathematical Analysis, Volume 43 (2011) no. 2, p. 764 | DOI:10.1137/100806746
Huang, Xiangdi; Li, Jing; Xin, Zhouping Serrin-Type Criterion for the Three-Dimensional Viscous Compressible Flows, SIAM Journal on Mathematical Analysis, Volume 43 (2011) no. 4, p. 1872 | DOI:10.1137/100814639
Sun, YongZhong; Zhang, ZhiFei A blow-up criterion of strong solutions to the 2D compressible Navier-Stokes equations, Science China Mathematics, Volume 54 (2011) no. 1, p. 105 | DOI:10.1007/s11425-010-4045-0
Charve, Frédéric; Danchin, Raphaël A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical L p Framework, Archive for Rational Mechanics and Analysis, Volume 198 (2010) no. 1, p. 233 | DOI:10.1007/s00205-010-0306-x
Chen, Qionglei; Miao, Changxing; Zhang, Zhifei Global well‐posedness for compressible Navier‐Stokes equations with highly oscillating initial velocity, Communications on Pure and Applied Mathematics, Volume 63 (2010) no. 9, p. 1173 | DOI:10.1002/cpa.20325
Amosova, E. V. Optimal control of the acceleration of a conducting gas, Journal of Applied and Industrial Mathematics, Volume 4 (2010) no. 1, p. 6 | DOI:10.1134/s1990478910010023
Wang, Changjia; Yuan, Hongjun Global strong solutions for a class of heat-conducting non-Newtonian fluids with vacuum, Nonlinear Analysis: Real World Applications, Volume 11 (2010) no. 5, p. 3680 | DOI:10.1016/j.nonrwa.2010.01.014
Danchin, Raphaël On the solvability of the compressible Navier–Stokes system in bounded domains, Nonlinearity, Volume 23 (2010) no. 2, p. 383 | DOI:10.1088/0951-7715/23/2/009
Jenssen, Helge Kristian; Karper, Trygve Klovning One-Dimensional Compressible Flow with Temperature Dependent Transport Coefficients, SIAM Journal on Mathematical Analysis, Volume 42 (2010) no. 2, p. 904 | DOI:10.1137/090763135
Fan, Jishan; Yu, Wanghui Strong solution to the compressible magnetohydrodynamic equations with vacuum, Nonlinear Analysis: Real World Applications, Volume 10 (2009) no. 1, p. 392 | DOI:10.1016/j.nonrwa.2007.10.001
Rozanova, Olga Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier–Stokes equations, Journal of Differential Equations, Volume 245 (2008) no. 7, p. 1762 | DOI:10.1016/j.jde.2008.07.007
Danchin, R. Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density, Communications in Partial Differential Equations, Volume 32 (2007) no. 9, p. 1373 | DOI:10.1080/03605300600910399
Rozanova, O. S. Formation of singularities of solutions of the equations of motion of compressible fluids subjected to external forces in the case of several spatial variables, Journal of Mathematical Sciences, Volume 143 (2007) no. 4, p. 3355 | DOI:10.1007/s10958-007-0214-2
Cho, Yonggeun; Kim, Hyunseok Existence results for viscous polytropic fluids with vacuum, Journal of Differential Equations, Volume 228 (2006) no. 2, p. 377 | DOI:10.1016/j.jde.2006.05.001
Gatapov, B. V.; Kazhikhov, A. V. Existence of a Global Solution to One Model Problem of Atmosphere Dynamics, Siberian Mathematical Journal, Volume 46 (2005) no. 5, p. 805 | DOI:10.1007/s11202-005-0079-x
Cho, Yonggeun; Choe, Hi Jun; Kim, Hyunseok Unique solvability of the initial boundary value problems for compressible viscous fluids, Journal de Mathématiques Pures et Appliquées, Volume 83 (2004) no. 2, p. 243 | DOI:10.1016/j.matpur.2003.11.004
Buccellato, Stefania; Yashima, Hisao Fujita Système d'équations d'un gaz visqueux modélisant l'atmosphère avec la force de Coriolis et la stabilité de l'état d'équilibre, ANNALI DELL UNIVERSITA DI FERRARA, Volume 49 (2003) no. 1, p. 127 | DOI:10.1007/bf02844913
Wang, Dehua Global solutions of the Navier–Stokes equations for viscous compressible flows, Nonlinear Analysis: Theory, Methods Applications, Volume 52 (2003) no. 8, p. 1867 | DOI:10.1016/s0362-546x(02)00280-8
Wang, Dehua On the global solution and interface behaviour of viscous compressible real flow with free boundaries, Nonlinearity, Volume 16 (2003) no. 2, p. 719 | DOI:10.1088/0951-7715/16/2/321
Wang, Dehua Large Solutions to the Initial-Boundary Value Problem for Planar Magnetohydrodynamics, SIAM Journal on Applied Mathematics, Volume 63 (2003) no. 4, p. 1424 | DOI:10.1137/s0036139902409284
Hsiao, Ling; Jiang, Song Chapter 4 Nonlinear hyperbolic—parabolic coupled systems, Volume 1 (2002), p. 287 | DOI:10.1016/s1874-5717(04)80006-9
Feireisl, Eduard Viscous and/or Heat Conducting Compressible Fluids, Volume 1 (2002), p. 307 | DOI:10.1016/s1874-5792(02)80010-6
Friedlander, Susan; Serre, Denis Preface, Volume 1 (2002), p. v | DOI:10.1016/s1874-5792(02)80001-5
Chen, Gui-Qiang; Wang, Dehua Global Solutions of Nonlinear Magnetohydrodynamics with Large Initial Data, Journal of Differential Equations, Volume 182 (2002) no. 2, p. 344 | DOI:10.1006/jdeq.2001.4111
Danchin, Raphaël LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES, Communications in Partial Differential Equations, Volume 26 (2001) no. 7-8, p. 1183 | DOI:10.1081/pde-100106132
References, Nonlinear Wave Equations Perturbed by Viscous Terms (2000), p. 239 | DOI:10.1515/9783110811902.239
Guo, Boling; Zhu, Peicheng Asymptotic Behavior of the Solution to the System for a Viscous Reactive Gas, Journal of Differential Equations, Volume 155 (1999) no. 1, p. 177 | DOI:10.1006/jdeq.1998.3578
Mamontov, A E Existence of global solutions of multidimensional Burgers's equations of a compressible viscous fluid, Sbornik: Mathematics, Volume 190 (1999) no. 8, p. 1131 | DOI:10.1070/sm1999v190n08abeh000420
Mamontov, A. E. Global solvability of the multidimensional Navier-Stokes equations of a compressible fluid with nonlinear viscosity. I, Siberian Mathematical Journal, Volume 40 (1999) no. 2, p. 351 | DOI:10.1007/s11202-999-0014-7
Мамонтов, Александр Евгеньевич; Mamontov, Alexander Evgenievich Существование глобальных решений многомерных уравнений Бюргерса сжимаемой вязкой жидкости, Математический сборник, Volume 190 (1999) no. 8, p. 61 | DOI:10.4213/sm420
Tonel, Laura On existence of global solutions to the Navier-Stokes equations for compressible and viscous flows on the surface of a sphere, ANNALI DELL UNIVERSITA DI FERRARA, Volume 44 (1998) no. 1, p. 63 | DOI:10.1007/bf02828017
Lu, Yun-Guang Existence of a Global Solution for a Viscoelastic System, Journal of Mathematical Analysis and Applications, Volume 218 (1998) no. 1, p. 175 | DOI:10.1006/jmaa.1997.5754
Jäger, W.; Lu, Yunguang Global Regularity of Solution for General Degenerate Parabolic Equations in 1-D, Journal of Differential Equations, Volume 140 (1997) no. 2, p. 365 | DOI:10.1006/jdeq.1997.3313
Solonnikov, V. A. The solvability of the initial boundary-value problem for equations of motion of a viscous compressible barotropic liquid in the spacesW 2 l+1,l/2+1 (Q T ), Journal of Mathematical Sciences, Volume 77 (1995) no. 3, p. 3250 | DOI:10.1007/bf02364719
Kazhikhov, A. V. The equation of potential flows of a compressible viscous fluid at small reynolds numbers: Existence, uniqueness, and stabilization of solutions, Siberian Mathematical Journal, Volume 34 (1993) no. 3, p. 457 | DOI:10.1007/bf00971220
Literature, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, Volume 22 (1990), p. 297 | DOI:10.1016/s0168-2024(08)70075-4
Mannucci, Paola A combustion problem in cylindrical and spherical symmetry, Meccanica, Volume 25 (1990) no. 1, p. 47 | DOI:10.1007/bf02015035
Padula, Mariarosaria Existence and uniqueness for viscous steady compressible motions, Archive for Rational Mechanics and Analysis, Volume 97 (1987) no. 2, p. 89 | DOI:10.1007/bf00251910
Valli, Alberto; Zajaczkowski, Wojciech M. Navier-stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case, Communications in Mathematical Physics, Volume 103 (1986) no. 2, p. 259 | DOI:10.1007/bf01206939
Neustupa, J. The global existence of weak solutions of the mollified system of equations of motion of viscous compressible fluid, Equadiff 6, Volume 1192 (1986), p. 409 | DOI:10.1007/bfb0076101
Nagasawa, Takeyuki On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary, Journal of Differential Equations, Volume 65 (1986) no. 1, p. 49 | DOI:10.1016/0022-0396(86)90041-0
Nishida, Takaaki Equations of Motion of Compressible Viscous Fluids, Patterns and Waves - Qualitative Analysis of Nonlinear Differential Equations, Volume 18 (1986), p. 97 | DOI:10.1016/s0168-2024(08)70129-2
Hoff, David Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 103 (1986) no. 3-4, p. 301 | DOI:10.1017/s0308210500018953
Bebernes, J.; Bressan, A. Global a priori estimates for a viscous reactive gas, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 101 (1985) no. 3-4, p. 321 | DOI:10.1017/s0308210500020862
Lagha-Benabdallah, A. Limites des equations d’un fluide compressible lorsque la compressibilite tend vers zero, Fluid Dynamics, Volume 1047 (1984), p. 139 | DOI:10.1007/bfb0072329
Fiszdon, W.; Zajaczkowski, W. M.; Gilbert, R. P. The Initial Boundary Value Problem for the Flow of a Barotropic Viscous Fluid, Global in Time, Applicable Analysis, Volume 15 (1983) no. 1-4, p. 91 | DOI:10.1080/00036818308839441
Hui, Shih Wei On the Cauchy Problem for the Equation of a General Fluid, Bifurcation Theory, Mechanics and Physics (1983), p. 109 | DOI:10.1007/978-94-009-7192-9_6
Valli, Alberto An existence theorem for compressible viscous fluids, Annali di Matematica Pura ed Applicata, Volume 130 (1982) no. 1, p. 197 | DOI:10.1007/bf01761495
Ton, Bui An On the initial-boundary value problem for viscous heat conducting compressible fluids, Kodai Mathematical Journal, Volume 4 (1981) no. 1 | DOI:10.2996/kmj/1138036314
Padula, Mariarosaria Existence and continuous dependence for solutions to the equations of a one-dimensional model in gas-dynamics, Meccanica, Volume 16 (1981) no. 3, p. 128 | DOI:10.1007/bf02128441
Ton, Bui An Existence and Uniqueness of a Classical Solution of an Initial-Boundary Value Problem of the Theory of Shallow Waters, SIAM Journal on Mathematical Analysis, Volume 12 (1981) no. 2, p. 229 | DOI:10.1137/0512022
Solonnikov, V. A. Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluid, Journal of Soviet Mathematics, Volume 14 (1980) no. 2, p. 1120 | DOI:10.1007/bf01562053
Ton, Bui An On the initial value problem for compressible fluid flows with vanishing viscosity, Kodai Mathematical Journal, Volume 3 (1980) no. 1 | DOI:10.2996/kmj/1138036123
Kanel', Ya. I. Cauchy problem for the equations of gasdynamics with viscosity, Siberian Mathematical Journal, Volume 20 (1979) no. 2, p. 208 | DOI:10.1007/bf00970025
Kato, Tosio Quasi-linear equations of evolution, with applications to partial differential equations, Spectral Theory and Differential Equations, Volume 448 (1975), p. 25 | DOI:10.1007/bfb0067080

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