Global solutions of the Cauchy problem for a viscous polytropic ideal gas

Song Jiang

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 1, page 47-74
  • ISSN: 0391-173X

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Jiang, Song. "Global solutions of the Cauchy problem for a viscous polytropic ideal gas." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.1 (1998): 47-74. <http://eudml.org/doc/84323>.

@article{Jiang1998,
author = {Jiang, Song},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {viscous polytropic gas; Cauchy problem; global solution; compressible Navier-Stokes equations; effective viscous flux},
language = {eng},
number = {1},
pages = {47-74},
publisher = {Scuola normale superiore},
title = {Global solutions of the Cauchy problem for a viscous polytropic ideal gas},
url = {http://eudml.org/doc/84323},
volume = {26},
year = {1998},
}

TY - JOUR
AU - Jiang, Song
TI - Global solutions of the Cauchy problem for a viscous polytropic ideal gas
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 1
SP - 47
EP - 74
LA - eng
KW - viscous polytropic gas; Cauchy problem; global solution; compressible Navier-Stokes equations; effective viscous flux
UR - http://eudml.org/doc/84323
ER -

References

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  1. [1] R.A. Adams, "Sobolev Spaces", Academic Press, New York, 1975. Zbl0314.46030MR450957
  2. [2] S.N. Antontsev - A.V. Kazhikhov - V.N. Monakhov, "Boundary Value Problems in Mechanics of Nonhomogeneous Fluids", North-Holland, Amsterdam, New York, 1990. Zbl0696.76001MR1035212
  3. [3] G.K. Batchelor, "An Introduction to Fluid Dynamics", Cambridge Univ. Press, London, 1967. Zbl0152.44402MR1744638
  4. [4] K. Deckelnick, Decay estimates for the compressible Navier-Stokes equations in unbounded domains, Math. Z.209 (1992), 115-130. Zbl0752.35048MR1143218
  5. [5] K. Deckelnick, L2 Decay for the compressible Navier-Stokes equations in unbounded domains, Comm. Partial Differential Equations18 (1993), 1445-1476. Zbl0798.35124MR1239919
  6. [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. Zbl0788.76070MR1244537
  7. [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. Zbl0881.76080MR1378239
  8. [8] E. Gagliardo, Ulteriori proprietà di alcune classi di funzioni in più variabili, Ricerche Mat.8 (1959), 21-51. Zbl0199.44701MR109295
  9. [9] D. Hoff, Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data, J. Differential Equations120 (1995), 215-254. Zbl0836.35120MR1339675
  10. [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. Zbl0836.76082MR1360077
  11. [11] S. Jiang, Large-time behavior of solutions to the equations of a viscous polytropic ideal gas, Ann. Mat. Pura Appl. (to appear). Zbl0953.35119MR1748226
  12. [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. Zbl0858.76069MR1389908
  13. [13] S. Kawashima, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Thesis, Kyoto University, 1983. 
  14. [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. Zbl0806.76077MR1241169
  15. [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. Zbl0778.76086MR1226126
  16. [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. Zbl0781.76072MR1228976
  17. [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. Zbl0447.76053MR555060
  18. [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. Zbl0429.76040MR564670
  19. [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. Zbl0505.76083MR784652
  20. [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. Zbl0543.76099MR713680
  21. [21] A. Matsumura - M. Padula, Stability of stationary flow of compressible fluids subject to large external potential forces, SAACM2 (1992), 183-202. 
  22. [22] J. Nash, Le problème de Cauchy pour les équations différentielles d'unfluide général, Bull. Soc. Math. France90 (1962), 487-497. Zbl0113.19405MR149094
  23. [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). Zbl0513.76070
  24. [24] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci.13 (1959), 115-162. Zbl0088.07601MR109940
  25. [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. Zbl0719.73013MR919738
  26. [26] J. Serrin, Mathematical principles of classical fluid mechanics, "Handbuch der Physik" VIII/1, Springer-Verlag, Berlin, Heidelberg, New York, 1972, pp. 125-262. MR108116
  27. [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. Zbl0785.35074
  28. [28] E. Stein, "Singular Integrals and Differentiability Properties of Functions", Princeton Univ. Press, Princeton, New Jersey, 1970. Zbl0207.13501MR290095
  29. [29] A. Tani, On the first initial-boundary problem of compressible viscous fluid motion, Publ. Res. Inst. Math. Sci.13 (1977), 193-253. Zbl0366.35070
  30. [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. Zbl0877.35092MR1316938
  31. [31] V.A. Vaigant - A.V. Kazhikhov, Global solutions to the potential flow equations for a compressible viscous fluid at small Reynolds numbers, Differential Equations30 (1994), 935-947. Zbl0835.35111MR1312722
  32. [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. Zbl0860.35098MR1375428
  33. [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. Zbl0802.76068MR1204928
  34. [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. Zbl0611.76082MR826865
  35. [35] D. Hoff, Discontinuous solutions of the Navier-Stokes equations for multidimensional heat-conducting flows, Arch. Rational Mech. Anal. (to appear). Zbl0904.76074

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