Wellposedness and Stability Results for the Navier-Stokes Equations in 𝐑3
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 599-624. 
@article{AIHPC_2009__26_2_599_0,
     author = {Chemin, Jean-Yves and Gallagher, Isabelle},
     title = {Wellposedness and {Stability} {Results} for the {Navier-Stokes} {Equations} in $\mathbf {R}^3$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {599--624},
     publisher = {Elsevier},
     volume = {26},
     number = {2},
     year = {2009},
     doi = {10.1016/j.anihpc.2007.05.008},
     mrnumber = {2504045},
     zbl = {1165.35038},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.008/}
}
TY  - JOUR
AU  - Chemin, Jean-Yves
AU  - Gallagher, Isabelle
TI  - Wellposedness and Stability Results for the Navier-Stokes Equations in $\mathbf {R}^3$
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 599
EP  - 624
VL  - 26
IS  - 2
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.008/
DO  - 10.1016/j.anihpc.2007.05.008
LA  - en
ID  - AIHPC_2009__26_2_599_0
ER  - 
%0 Journal Article
%A Chemin, Jean-Yves
%A Gallagher, Isabelle
%T Wellposedness and Stability Results for the Navier-Stokes Equations in $\mathbf {R}^3$
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 599-624
%V 26
%N 2
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.008/
%R 10.1016/j.anihpc.2007.05.008
%G en
%F AIHPC_2009__26_2_599_0
Chemin, Jean-Yves; Gallagher, Isabelle. Wellposedness and Stability Results for the Navier-Stokes Equations in $\mathbf {R}^3$. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 599-624. doi : 10.1016/j.anihpc.2007.05.008. https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.008/

[1] Auscher P., Dubois S., Tchamitchian P., On the Stability of Global Solutions to Navier-Stokes Equations in the Space, Journal de Mathématiaques Pures et Appliquées 83 (2004) 673-697. | MR | Zbl

[2] Bahouri H., Chemin J.-Y., Gallagher I., Refined Hardy Inequalities, Annali di Scuola Normale di Pisa, Classe di Scienze, Serie V 5 (2006) 375-391. | Numdam | MR | Zbl

[3] Bahouri H., Gérard P., High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations, American Journal of Mathematics 121 (1999) 131-175. | MR | Zbl

[4] M. Cannone, Y. Meyer, F. Planchon, Solutions autosimilaires des équations de Navier-Stokes, Séminaire “Équations aux Dérivées Partielles” de l'École polytechnique, Exposé VIII, 1993-1994. | Numdam | MR | Zbl

[5] Chemin J.-Y., Fluides Parfaits Incompressibles, Astérisque, vol. 230, 1995, English translation: J.-Y. Chemin, Perfect Incompressible Fluids, Oxford University Press, 1998. | Numdam | MR | Zbl

[6] Chemin J.-Y., Théorèmes D'unicité Pour Le Système De Navier-Stokes Tridimensionnel, Journal d'Analyse Mathématique 77 (1999) 27-50. | MR | Zbl

[7] J.-Y. Chemin, Localization in Fourier space and Navier-Stokes system, in: Phase Space Analysis of Partial Differential Equations, Proceedings 2004, CRM series, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Normale di Pisa, pp. 53-136. | MR | Zbl

[8] Chemin J.-Y., Gallagher I., On the Global Wellposedness of the 3-D Navier-Stokes Equations With Large Initial Data, Annales Scientifiques de l'École Normale Supérieure de Paris 39 (4) (2006) 679-698. | Numdam | MR | Zbl

[9] Foias C., Saut J.-C., Asymptotic Behaviour, as t→∞, of Solutions of the Navier-Stokes Equations and Nonlinear Spectral Manifolds, Indiana Mathematical Journal 33 (3) (1984) 459-477. | MR | Zbl

[10] Fujita H., Kato T., On the Navier-Stokes Initial Value Problem I, Archive for Rational Mechanics and Analysis 16 (1964) 269-315. | MR | Zbl

[11] Gallagher I., The Tridimensional Navier-Stokes Equations With Almost Bidimensional Data: Stability, Uniqueness and Life Span, International Mathematical Research Notices 18 (1997) 919-935. | MR | Zbl

[12] Gallagher I., Profile Decomposition for the Navier-Stokes Equations, Bulletin de la Société Mathématique de France 129 (2001) 285-316. | Numdam | MR | Zbl

[13] Gallagher I., Iftimie D., Planchon F., Asymptotics and Stability for Global Solutions to the Navier-Stokes Equations, Annales de l'Institut Fourier 53 (5) (2003) 1387-1424. | Numdam | MR | Zbl

[14] Gérard P., Description Du Défaut De Compacité De L'injection De Sobolev, ESAIM Contrôle Optimal et Calcul des Variations 3 (1998) 213-233. | Numdam | MR | Zbl

[15] Giga Y., Miyakawa T., Solutions in Lr of the Navier-Stokes Initial Value Problem, Archive for Rational Mechanics and Analysis 89 (3) (1985) 267-281. | MR | Zbl

[16] Iftimie D., The 3D Navier-Stokes Equations Seen as a Perturbation of the 2D Navier-Stokes Equations, Bulletin de la Société Mathématique de France 127 (1999) 473-517. | Numdam | MR | Zbl

[17] Kato T., Strong Lp Solutions of the Navier-Stokes Equations in Rm With Applications to Weak Solutions, Mathematische Zeitschrift 187 (1984) 471-480. | MR | Zbl

[18] Koch H., Tataru D., Well-Posedness for the Navier-Stokes Equations, Advances in Mathematics 157 (2001) 22-35. | MR | Zbl

[19] Ladyzhenskaya O., The Mathematical Theory of Viscous Incompressible Flow, Mathematics and its Applications, vol. 2, Second English edition, revised and enlarged, Gordon and Breach, Science Publishers, New York-London-Paris, 1969, xviii+224 pp. | MR | Zbl

[20] Leibovich S., Mahalov A., Titi E., Invariant Helical Subspaces for the Navier-Stokes Equations, Archive for Rational Mechanics and Analysis 112 (3) (1990) 193-222. | MR | Zbl

[21] Lemarié-Rieusset P.-G., Recent Developments in the Navier-Stokes Problem, Research Notes in Mathematics, vol. 431, Chapman & Hall/CRC, 2002. | MR | Zbl

[22] Leray J., Essai Sur Le Mouvement D'un Liquide Visqueux Emplissant L'espace, Acta Matematica 63 (1933) 193-248. | JFM | MR

[23] Ponce G., Racke R., Sideris T., Titi E., Global Stability of Large Solutions to the 3D Navier-Stokes Equations, Communitacions in Mathematical Physics 159 (1994). | MR | Zbl

[24] Ukhovskii M., Iudovich V., Axially Symmetric Flows of Ideal and Viscous Fluids Filling the Whole Space, Prikladnaya Matematika i Mekhanika 32 (1968) 59-69, (in Russian); translated as, Journal of Applied Mathematics and Mechanics 32 (1968) 52-61. | MR | Zbl

  • Bie, Qunyi; Chen, Hao On almost axisymmetric incompressible magnetohydrodynamics in three dimensions, Acta Mathematica Scientia, Volume 45 (2025) no. 2, p. 446 | DOI:10.1007/s10473-025-0210-y
  • Deng, Wen; Paicu, Marius Gevrey regularity for the subcritical dissipative generalized surface quasi-geostrophic equations, Mathematische Zeitschrift, Volume 309 (2025) no. 4 | DOI:10.1007/s00209-025-03692-z
  • Zhao, Jihong Global existence of large solutions for the parabolic–elliptic Keller–Segel system in Besov type spaces, Applied Mathematics Letters, Volume 149 (2024), p. 108899 | DOI:10.1016/j.aml.2023.108899
  • Liu, Wenjuan; Peng, Jialing Analyticity estimates for the 3D magnetohydrodynamic equations, Electronic Research Archive, Volume 32 (2024) no. 6, p. 3819 | DOI:10.3934/era.2024173
  • Ciampa, Gennaro; Lucà, Renato Localization of Beltrami fields: Global smooth solutions and vortex reconnection for the Navier-Stokes equations, Journal of Functional Analysis, Volume 287 (2024) no. 9, p. 110610 | DOI:10.1016/j.jfa.2024.110610
  • Zhao, Jihong; Jin, Rong; Chen, Hao Global existence of solutions for the drift–diffusion system with large initial data in Ḃ−2∞,∞ (Rd), Nonlinear Analysis: Real World Applications, Volume 80 (2024), p. 104145 | DOI:10.1016/j.nonrwa.2024.104145
  • Hao, Xiaonan; Li, Zhen Large global solutions to 3D Boussinesq equations slowly varying in one direction, Zeitschrift für angewandte Mathematik und Physik, Volume 75 (2024) no. 3 | DOI:10.1007/s00033-024-02228-5
  • Zhai, Xiaoping; Zhong, Xin Global Solutions to the 2D Compressible Navier-Stokes Equations with Some Large Initial Data, Acta Mathematica Scientia, Volume 43 (2023) no. 3, p. 1251 | DOI:10.1007/s10473-023-0315-0
  • Li, Rulv Smooth solution for incompressible Navier–Stokes equations with large initial, Applicable Analysis, Volume 102 (2023) no. 10, p. 2866 | DOI:10.1080/00036811.2022.2040995
  • Zhai, Xiaoping; Chen, Yiren; Li, Yongsheng Large global solutions of the compressible Navier-Stokes equations in three dimensions, Discrete and Continuous Dynamical Systems, Volume 43 (2023) no. 1, p. 309 | DOI:10.3934/dcds.2022150
  • Yang, Haibo; Yang, Qixiang; Wu, Huoxiong Middle frequency band and remark on Koch–Tataru’s iteration space, International Journal of Wavelets, Multiresolution and Information Processing, Volume 21 (2023) no. 04 | DOI:10.1142/s0219691323500030
  • Yang, Qixiang; Yang, Haibo; Hon, Chitin Distribution of large value points via frequency and wellposedness of Navier-Stokes equations, Journal of Differential Equations, Volume 376 (2023), p. 574 | DOI:10.1016/j.jde.2023.08.036
  • Zhang, Fan; Xu, Fuyi; Fu, Peng The Global Solvability of the Non-conservative Viscous Compressible Two-Fluid Model with Capillarity Effects for Some Large Initial Data, Journal of Mathematical Fluid Mechanics, Volume 25 (2023) no. 3 | DOI:10.1007/s00021-023-00797-5
  • Zhang, Ping On the instantaneous radius of analyticity of Lp solutions to 3D Navier–Stokes system, Mathematische Zeitschrift, Volume 304 (2023) no. 3 | DOI:10.1007/s00209-023-03301-x
  • Luo, Wei; Ye, Weikui; Yin, Zhaoyang The Continuous Dependence for the Navier–Stokes Equations in B˙p,rdp−1, Results in Mathematics, Volume 78 (2023) no. 6 | DOI:10.1007/s00025-023-02004-3
  • Yu, Yanghai; Li, Jinlu; Yin, Zhaoyang Global solutions to 3D incompressible Navier–Stokes equations with some large initial data, Applied Mathematics Letters, Volume 129 (2022), p. 107954 | DOI:10.1016/j.aml.2022.107954
  • Hu, Ruilin; Zhang, Ping On the Radius of Analyticity of Solutions to 3D Navier-Stokes System with Initial Data in Lp, Chinese Annals of Mathematics, Series B, Volume 43 (2022) no. 5, p. 749 | DOI:10.1007/s11401-022-0356-z
  • Liu, Lvqiao On the global existence to Hall-MHD system, Discrete and Continuous Dynamical Systems - B, Volume 27 (2022) no. 12, p. 7301 | DOI:10.3934/dcdsb.2022044
  • Zhang, Huali A class of global large, smooth solutions for the magnetohydrodynamics with Hall and ion‐slip effects, Mathematical Methods in the Applied Sciences, Volume 45 (2022) no. 10, p. 5721 | DOI:10.1002/mma.8136
  • Chen, Qionglei; Hao, Xiaonan Local and some type of large solutions for the chemotaxis-fluid equations with partial dissipation, Nonlinear Analysis, Volume 217 (2022), p. 112746 | DOI:10.1016/j.na.2021.112746
  • Yomgne Diebou, Gael Well-posedness for chemotaxis–fluid models in arbitrary dimensions*, Nonlinearity, Volume 35 (2022) no. 12, p. 6241 | DOI:10.1088/1361-6544/ac98ec
  • Wang, Peng; Guo, Zhengguang Global Axisymmetric Solutions to the 3D MHD Equations with Nonzero Swirl, The Journal of Geometric Analysis, Volume 32 (2022) no. 10 | DOI:10.1007/s12220-022-01006-x
  • Zhang, Shunhang Global Large Solutions to the 3-D Generalized Incompressible Navier–Stokes Equations, Bulletin of the Malaysian Mathematical Sciences Society, Volume 44 (2021) no. 4, p. 2101 | DOI:10.1007/s40840-020-01051-1
  • Farwig, Reinhard From Jean Leray to the millennium problem: the Navier–Stokes equations, Journal of Evolution Equations, Volume 21 (2021) no. 3, p. 3243 | DOI:10.1007/s00028-020-00645-3
  • Jlali, Lotfi Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces, Open Mathematics, Volume 19 (2021) no. 1, p. 898 | DOI:10.1515/math-2021-0060
  • Xi, Xuan-Xuan; Hou, Mimi; Zhou, Xian-Feng; Wen, Yanhua Approximate controllability for mild solution of time-fractional Navier–Stokes equations with delay, Zeitschrift für angewandte Mathematik und Physik, Volume 72 (2021) no. 3 | DOI:10.1007/s00033-021-01542-6
  • Ye, Hailong; Jia, Yan Long-time behaviors for the Navier–Stokes equations under large initial perturbation, Zeitschrift für angewandte Mathematik und Physik, Volume 72 (2021) no. 4 | DOI:10.1007/s00033-021-01569-9
  • Wu, Di Blow-Up Criterion and Examples of Global Solutions of Forced Navier-Stokes Equations, Acta Applicandae Mathematicae, Volume 170 (2020) no. 1, p. 99 | DOI:10.1007/s10440-020-00326-w
  • Zhai, Xiaoping; Yin, Zhaoyang On some large global solutions to the incompressible inhomogeneous nematic liquid crystal flows, Applicable Analysis, Volume 99 (2020) no. 6, p. 959 | DOI:10.1080/00036811.2018.1515923
  • Liu, Qiao Global Well-Posedness of the Generalized Incompressible Navier–Stokes Equations with Large Initial Data, Bulletin of the Malaysian Mathematical Sciences Society, Volume 43 (2020) no. 3, p. 2549 | DOI:10.1007/s40840-019-00818-5
  • Zhang, Shunhang A class of global large solutions to the compressible Navier–Stokes–Korteweg system in critical Besov spaces, Journal of Evolution Equations, Volume 20 (2020) no. 4, p. 1531 | DOI:10.1007/s00028-020-00565-2
  • Benameur, Jamel; Jlali, Lotfi Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces, Mathematica Slovaca, Volume 70 (2020) no. 4, p. 877 | DOI:10.1515/ms-2017-0400
  • Wang, Weihua Global existence and analyticity of mild solutions for the stochastic Navier–Stokes–Coriolis equations in Besov spaces, Nonlinear Analysis: Real World Applications, Volume 52 (2020), p. 103048 | DOI:10.1016/j.nonrwa.2019.103048
  • 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
  • Xu, Liyang; Shen, Tianlong; Yang, Xuejun; Liang, Jiarui Analysis of time fractional and space nonlocal stochastic incompressible Navier–Stokes equation driven by white noise, Computers Mathematics with Applications, Volume 78 (2019) no. 5, p. 1669 | DOI:10.1016/j.camwa.2018.12.022
  • Lewandowski, Roger Navier-Stokes equations in the whole space with an eddy viscosity, Journal of Mathematical Analysis and Applications, Volume 478 (2019) no. 2, p. 698 | DOI:10.1016/j.jmaa.2019.05.051
  • Chikami, Noboru; Kobayashi, Takayuki Global Well-Posedness and Time-Decay Estimates of the Compressible Navier–Stokes–Korteweg System in Critical Besov Spaces, Journal of Mathematical Fluid Mechanics, Volume 21 (2019) no. 2 | DOI:10.1007/s00021-019-0431-8
  • Chemin, Jean-Yves; Gallagher, Isabelle A nonlinear estimate of the life span of solutions of the three dimensional Navier–Stokes equations, Tunisian Journal of Mathematics, Volume 1 (2019) no. 2, p. 273 | DOI:10.2140/tunis.2019.1.273
  • Wang, Weihua Global well-posedness and analyticity for the 3D fractional magnetohydrodynamics equations in variable Fourier–Besov spaces, Zeitschrift für angewandte Mathematik und Physik, Volume 70 (2019) no. 6 | DOI:10.1007/s00033-019-1210-3
  • ZHANG, Jianlin; QIN, Yuming Exact solutions for the Cauchy problem to the 3D spherically symmetric incompressible Navier-Stokes equations, Acta Mathematica Scientia, Volume 38 (2018) no. 3, p. 778 | DOI:10.1016/s0252-9602(18)30783-5
  • Wang, Wei Hua; Wu, Gang Global Mild Solution of Stochastic Generalized Navier–Stokes Equations with Coriolis Force, Acta Mathematica Sinica, English Series, Volume 34 (2018) no. 11, p. 1635 | DOI:10.1007/s10114-018-7482-2
  • Wang, Wei Hua; Wu, Gang Global well-posedness of the 3D generalized rotating magnetohydrodynamics equations, Acta Mathematica Sinica, English Series, Volume 34 (2018) no. 6, p. 992 | DOI:10.1007/s10114-017-7276-y
  • Duan, Ning Well-posedness and decay of solutions for three-dimensional generalized Navier–Stokes equations, Computers Mathematics with Applications, Volume 76 (2018) no. 5, p. 1026 | DOI:10.1016/j.camwa.2018.05.038
  • Brandolese, Lorenzo; Schonbek, Maria E. Large Time Behavior of the Navier-Stokes Flow, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 579 | DOI:10.1007/978-3-319-13344-7_11
  • Gallagher, Isabelle Critical Function Spaces for the Well-Posedness of the Navier-Stokes Initial Value Problem, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2018), p. 647 | DOI:10.1007/978-3-319-13344-7_12
  • D’Ancona, Piero; Lucà, Renato Stability Properties of the Regular Set for the Navier–Stokes Equation, Journal of Mathematical Fluid Mechanics, Volume 20 (2018) no. 2, p. 819 | DOI:10.1007/s00021-017-0349-y
  • Liu, Qiao Global Well-Posedness and Temporal Decay Estimates for the 3D Nematic Liquid Crystal Flows, Journal of Mathematical Fluid Mechanics, Volume 20 (2018) no. 4, p. 1459 | DOI:10.1007/s00021-018-0373-6
  • Zhai, Cuili Global solutions for the 3-D incompressible nonhomogeneous MHD equations, Nonlinear Analysis, Volume 169 (2018), p. 163 | DOI:10.1016/j.na.2017.12.011
  • Haspot, Boris Global existence of strong solution for viscous shallow water system with large initial data on the irrotational part, Journal of Differential Equations, Volume 262 (2017) no. 10, p. 4931 | DOI:10.1016/j.jde.2017.01.010
  • Liu, Hui; Gao, Hongjun Global well-posedness and long time decay of the 3D Boussinesq equations, Journal of Differential Equations, Volume 263 (2017) no. 12, p. 8649 | DOI:10.1016/j.jde.2017.08.049
  • Xu, Huan; Li, Yongsheng; Chen, Fei Global Solution to the Incompressible Inhomogeneous Navier–Stokes Equations with Some Large Initial Data, Journal of Mathematical Fluid Mechanics, Volume 19 (2017) no. 2, p. 315 | DOI:10.1007/s00021-016-0282-5
  • Qin, Yuming; Zhang, Jianlin Asymptotic behavior of exact solutions for the Cauchy problem to the 3D cylindrically symmetric Navier–Stokes equations, Mathematical Methods in the Applied Sciences, Volume 40 (2017) no. 12, p. 4538 | DOI:10.1002/mma.4324
  • Yang, Minghua Global solutions to Keller‐Segel‐Navier‐Stokes equations with a class of large initial data in critical Besov spaces, Mathematical Methods in the Applied Sciences, Volume 40 (2017) no. 18, p. 7425 | DOI:10.1002/mma.4538
  • Jlali, Lotfi Global well posedness of 3D‐NSE in Fourier–Lei–Lin spaces, Mathematical Methods in the Applied Sciences, Volume 40 (2017) no. 7, p. 2713 | DOI:10.1002/mma.4193
  • Brandolese, Lorenzo; Schonbek, Maria E. Large Time Behavior of the Navier–Stokes Flow, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_11-1
  • Gallagher, Isabelle Critical Function Spaces for the Wellposedness of the Navier-Stokes Initial Value Problem, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (2016), p. 1 | DOI:10.1007/978-3-319-10151-4_12-1
  • Chemin, Jean-Yves; David, Claire From an Initial Data to a Global Solution of the Non-linear Schrödinger Equation: A Building Process, International Mathematics Research Notices, Volume 2016 (2016) no. 8, p. 2376 | DOI:10.1093/imrn/rnv199
  • Lin, Yurui; Zhang, Huali; Zhou, Yi Global smooth solutions of MHD equations with large data, Journal of Differential Equations, Volume 261 (2016) no. 1, p. 102 | DOI:10.1016/j.jde.2016.03.002
  • Haspot, Boris Existence of global strong solution for Korteweg system with large infinite energy initial data, Journal of Mathematical Analysis and Applications, Volume 438 (2016) no. 1, p. 395 | DOI:10.1016/j.jmaa.2016.01.047
  • Zaja̧czkowski, W.M. Stability of two-dimensional solutions to the Navier–Stokes equations in cylindrical domains under Navier boundary conditions, Journal of Mathematical Analysis and Applications, Volume 444 (2016) no. 1, p. 275 | DOI:10.1016/j.jmaa.2016.05.059
  • Jia, Junxiong; Peng, Jigen; Gao, Jinghuai Well-posedness for compressible MHD systems with highly oscillating initial data, Journal of Mathematical Physics, Volume 57 (2016) no. 8 | DOI:10.1063/1.4961157
  • Lucà, Renato On the size of the regular set of suitable weak solutions of the Navier–Stokes equation, Journées équations aux dérivées partielles (2016), p. 1 | DOI:10.5802/jedp.634
  • Dong, Bo-Qing; Jia, Yan Stability behaviors of Leray weak solutions to the three-dimensional Navier–Stokes equations, Nonlinear Analysis: Real World Applications, Volume 30 (2016), p. 41 | DOI:10.1016/j.nonrwa.2015.10.011
  • Lewandowski, Roger; Pinier, Benoît The Kolmogorov Law of Turbulence What Can Rigorously Be Proved? Part II, The Foundations of Chaos Revisited: From Poincaré to Recent Advancements (2016), p. 71 | DOI:10.1007/978-3-319-29701-9_5
  • Bibliography, The Navier-Stokes Problem in the 21st Century (2016), p. 677 | DOI:10.1201/b19556-23
  • Chen, Fei; Li, Yongsheng; Xu, Huan Global solution to the 3D nonhomogeneous incompressible MHD equations with some large initial data, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 6, p. 2945 | DOI:10.3934/dcds.2016.36.2945
  • Benameur, Jamel Long time decay to the Lei–Lin solution of 3D Navier–Stokes equations, Journal of Mathematical Analysis and Applications, Volume 422 (2015) no. 1, p. 424 | DOI:10.1016/j.jmaa.2014.08.039
  • Ge, Yuli; Shao, Shuguang Global solution of 3D incompressible magnetohydrodynamics equations with finite energy, Journal of Mathematical Analysis and Applications, Volume 422 (2015) no. 1, p. 571 | DOI:10.1016/j.jmaa.2014.09.003
  • Zadrzyńska, Ewa; Zaja̧czkowski, Wojciech M. Stability of two-dimensional Navier–Stokes motions in the periodic case, Journal of Mathematical Analysis and Applications, Volume 423 (2015) no. 2, p. 956 | DOI:10.1016/j.jmaa.2014.10.026
  • Wong, Percy Global Wellposedness for a Certain Class of Large Initial Data for the 3D Navier–Stokes Equations, Annales Henri Poincaré, Volume 15 (2014) no. 4, p. 633 | DOI:10.1007/s00023-013-0255-7
  • Zhang, Ping; Zhang, Ting Global Axisymmetric Solutions to Three-Dimensional Navier–Stokes System, International Mathematics Research Notices, Volume 2014 (2014) no. 3, p. 610 | DOI:10.1093/imrn/rns232
  • Paicu, Marius; Zhang, Zhifei Global well-posedness for 3D Navier–Stokes equations with ill-prepared initial data, Journal of the Institute of Mathematics of Jussieu, Volume 13 (2014) no. 2, p. 395 | DOI:10.1017/s1474748013000212
  • Wang, Yuzhu; Wang, Keyan Global well-posedness of the three dimensional magnetohydrodynamics equations, Nonlinear Analysis: Real World Applications, Volume 17 (2014), p. 245 | DOI:10.1016/j.nonrwa.2013.12.002
  • Zhang, Ting Global strong solutions for equations related to the incompressible viscoelastic fluids with a class of large initial data, Nonlinear Analysis: Theory, Methods Applications, Volume 100 (2014), p. 59 | DOI:10.1016/j.na.2014.01.014
  • Tao, Terence Localisation and compactness properties of the Navier–Stokes global regularity problem, Analysis PDE, Volume 6 (2013) no. 1, p. 25 | DOI:10.2140/apde.2013.6.25
  • Bahouri, Hajer; Gallagher, Isabelle On the Stability in Weak Topology of the Set of Global Solutions to the Navier–Stokes Equations, Archive for Rational Mechanics and Analysis, Volume 209 (2013) no. 2, p. 569 | DOI:10.1007/s00205-013-0623-y
  • Haspot, Boris Existence of global strong solutions for the barotropic Navier–Stokes system with large initial data on the rotational part of the velocity, Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, p. 487 | DOI:10.1016/j.crma.2012.04.017
  • Paicu, Marius; Zhang, Ping Global solutions to the 3-D incompressible inhomogeneous Navier–Stokes system, Journal of Functional Analysis, Volume 262 (2012) no. 8, p. 3556 | DOI:10.1016/j.jfa.2012.01.022
  • Han, Jinsheng Large global well‐posedness of the three‐dimensional magneto‐hydrodynamic equations with the initial data of the type ‘v + w’, Mathematical Methods in the Applied Sciences, Volume 35 (2012) no. 17, p. 2036 | DOI:10.1002/mma.2634
  • Zhang, Ting; Fang, Daoyuan Global Existence of Strong Solution for Equations Related to the Incompressible Viscoelastic Fluids in the Critical Lp Framework, SIAM Journal on Mathematical Analysis, Volume 44 (2012) no. 4, p. 2266 | DOI:10.1137/110851742
  • Paicu, Marius; Zhang, Zhifei Global regularity for the Navier–Stokes equations with some classes of large initial data, Analysis PDE, Volume 4 (2011) no. 1, p. 95 | DOI:10.2140/apde.2011.4.95
  • Chemin, Jean-Yves; Gallagher, Isabelle; Paicu, Marius Global regularity for some classes of large solutions to the Navier-Stokes equations, Annals of Mathematics, Volume 173 (2011) no. 2, p. 983 | DOI:10.4007/annals.2011.173.2.9
  • Lei, Zhen; Lin, Fang‐Hua Global mild solutions of Navier‐Stokes equations, Communications on Pure and Applied Mathematics, Volume 64 (2011) no. 9, p. 1297 | DOI:10.1002/cpa.20361
  • Abidi, Hammadi; Hmidi, Taoufik; Keraani, Sahbi On the global regularity of axisymmetric Navier-Stokes-Boussinesq system, Discrete Continuous Dynamical Systems - A, Volume 29 (2011) no. 3, p. 737 | DOI:10.3934/dcds.2011.29.737
  • Hmidi, Taoufik; Rousset, Frédéric Global well-posedness for the Navier–Stokes–Boussinesq system with axisymmetric data, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 27 (2010) no. 5, p. 1227 | DOI:10.1016/j.anihpc.2010.06.001
  • Zhang, Ting Global Wellposed Problem for the 3-D Incompressible Anisotropic Navier-Stokes Equations in an Anisotropic Space, Communications in Mathematical Physics, Volume 287 (2009) no. 1, p. 211 | DOI:10.1007/s00220-008-0631-1
  • Zhang, Ting; Fang, Daoyuan Global wellposed problem for the 3-D incompressible anisotropic Navier–Stokes equations, Journal de Mathématiques Pures et Appliquées, Volume 90 (2008) no. 5, p. 413 | DOI:10.1016/j.matpur.2008.06.008

Cité par 87 documents. Sources : Crossref