Global solutions of the Cauchy problem for a viscous polytropic ideal gas
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 26 (1998) no. 1, p. 47-74
@article{ASNSP_1998_4_26_1_47_0,
     author = {Jiang, Song},
     title = {Global solutions of the Cauchy problem for a viscous polytropic ideal gas},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {1},
     year = {1998},
     pages = {47-74},
     zbl = {0928.35134},
     mrnumber = {1632992},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_26_1_47_0}
}
Jiang, Song. Global solutions of the Cauchy problem for a viscous polytropic ideal gas. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 26 (1998) no. 1, pp. 47-74. http://www.numdam.org/item/ASNSP_1998_4_26_1_47_0/

[1] R.A. Adams, "Sobolev Spaces", Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[2] S.N. Antontsev - A.V. Kazhikhov - V.N. Monakhov, "Boundary Value Problems in Mechanics of Nonhomogeneous Fluids", North-Holland, Amsterdam, New York, 1990. | MR 1035212 | Zbl 0696.76001

[3] G.K. Batchelor, "An Introduction to Fluid Dynamics", Cambridge Univ. Press, London, 1967. | MR 1744638 | Zbl 0152.44402

[4] K. Deckelnick, Decay estimates for the compressible Navier-Stokes equations in unbounded domains, Math. Z. 209 (1992), 115-130. | MR 1143218 | Zbl 0752.35048

[5] K. Deckelnick, L2 Decay for the compressible Navier-Stokes equations in unbounded domains, Comm. Partial Differential Equations 18 (1993), 1445-1476. | MR 1239919 | Zbl 0798.35124

[6] H. Fujita-Yashima - R. Benabidallah, Unicité de la solution de l'équation monodimensionnelle ou à symétrie sphérique d'un gaz visqueux et calorifère, Rend. Circ. Mat. Palermo (2) 42 (1993), 195-218. | MR 1244537 | Zbl 0788.76070

[7] H. Fujita-Yashima - R. Benabidallah, Equation à symétrie sphérique d'un gaz visqueux et calorifère avec la surface libre, Ann. Mat. Pura Appl. 168 (1995), 75-117. | MR 1378239 | Zbl 0881.76080

[8] E. Gagliardo, Ulteriori proprietà di alcune classi di funzioni in più variabili, Ricerche Mat. 8 (1959), 21-51. | MR 109295 | Zbl 0199.44701

[9] D. Hoff, Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data, J. Differential Equations 120 (1995), 215-254. | MR 1339675 | Zbl 0836.35120

[10] D. Hoff, Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data, Arch. Rational Mech. Anal. 132 (1995), 1-14. | MR 1360077 | Zbl 0836.76082

[11] S. Jiang, Large-time behavior of solutions to the equations of a viscous polytropic ideal gas, Ann. Mat. Pura Appl. (to appear). | MR 1748226 | Zbl 0953.35119

[12] S. Jiang, Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain, Comm. Math. Phys. 178 (1996), 339-374. | MR 1389908 | Zbl 0858.76069

[13] S. Kawashima, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Thesis, Kyoto University, 1983.

[14] A.V. Kazhikhov, The equations of potential flows of a compressible viscous fluid at small Reynolds numbers: existence, uniqueness, and stabilization of solutions, Siberian Math. J. 34 (1993), 457-467. | MR 1241169 | Zbl 0806.76077

[15] P.-L. Lions, Existence globale de solutions pour les équations de Navier-Stokes compressibles isentropiques, C.R. Acad. Sci. Paris Sér. I-Math. 316 (1993), 1335-1340. | MR 1226126 | Zbl 0778.76086

[16] P.-L. Lions, Compacité des solutions des équations de Navier-Stokes compressibles isentropiques, C.R. Acad. Sci. Paris Sér. I-Math. 317 (1993), 115-120. | MR 1228976 | Zbl 0781.76072

[17] A. Matsumura - T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), 337-342. | MR 555060 | Zbl 0447.76053

[18] A. Matsumura - T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104. | MR 564670 | Zbl 0429.76040

[19] A. Matsumura - T. Nishida, Initial boundary value problems for the equations of motion of general fluids, in: Computing Methods in Applied. Sciences and Engineering, V, R. Glowinski, J. L. Lions (eds.), North-Holland, Amsterdam, 1982, pp. 389-406. | MR 784652 | Zbl 0505.76083

[20] A. Matsumura - T. Nishida, Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids, Comm. Math. Phys. 89 (1983), 445-464. | MR 713680 | Zbl 0543.76099

[21] A. Matsumura - M. Padula, Stability of stationary flow of compressible fluids subject to large external potential forces, SAACM 2 (1992), 183-202.

[22] J. Nash, Le problème de Cauchy pour les équations différentielles d'unfluide général, Bull. Soc. Math. France 90 (1962), 487-497. | Numdam | MR 149094 | Zbl 0113.19405

[23] V.B. Nikolaev, On the solvability of mixed problem for one-dimensional axisymmetrical viscous gas flow. Dinamicheskie zadachi Mekhaniki sploshnoj sredy, 63Sibirsk. Otd. Acad. Nauk SSSR, Inst. Gidrodinamiki, 1983 (Russian).

[24] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 13 (1959), 115-162. | Numdam | MR 109940 | Zbl 0088.07601

[25] M. Renardy - W.J. Hrusa - J.A. Nohel, " Mathematical Problems in Viscoelasticity", Pitman Monographs and Surveys in Pure and Appl. Math. 35, Longman, Harlow, 1987. | MR 919738 | Zbl 0719.73013

[26] J. Serrin, Mathematical principles of classical fluid mechanics, "Handbuch der Physik" VIII/1, Springer-Verlag, Berlin, Heidelberg, New York, 1972, pp. 125-262. | MR 108116

[27] R. Salvi - I. Stra, Global existence for viscous compressible fluids and their behavior as t → ∞, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40 (1993), 17-51. | Zbl 0785.35074

[28] E. Stein, "Singular Integrals and Differentiability Properties of Functions", Princeton Univ. Press, Princeton, New Jersey, 1970. | MR 290095 | Zbl 0207.13501

[29] A. Tani, On the first initial-boundary problem of compressible viscous fluid motion, Publ. Res. Inst. Math. Sci. 13 (1977), 193-253. | Zbl 0366.35070

[30] V.A. Vaigant, An example of nonexistence globally in time of a solution of the Navier-Stokes equations for a compressible viscous barotropic fluid, Russian Acad. Sci. Dokl. Math. 50 (1995), 397-399. | MR 1316938 | Zbl 0877.35092

[31] V.A. Vaigant - A.V. Kazhikhov, Global solutions to the potential flow equations for a compressible viscous fluid at small Reynolds numbers, Differential Equations 30 (1994), 935-947. | MR 1312722 | Zbl 0835.35111

[32] V.A. Vaigant - A.V. Kazhikhov, On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid, Siberian J. Math. 36 (1995), 1283-1316. | MR 1375428 | Zbl 0860.35098

[33] A. Valli, Mathematical results for compressible flows, in: "Mathematical Topics in Fluid Mechanics", J. F. Rodrigues and A. Sequeira (eds.), Pitman Research Notes in Math. Ser. 274, John Wiley, New York, 1992, pp. 193-229. | MR 1204928 | Zbl 0802.76068

[34] A. Valli - W.M. Zajaczkowski, Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case, Comm. Math. Phys. 103 (1986), 259-296. | MR 826865 | Zbl 0611.76082

[35] D. Hoff, Discontinuous solutions of the Navier-Stokes equations for multidimensional heat-conducting flows, Arch. Rational Mech. Anal. (to appear). | Zbl 0904.76074