Regularity of weak solutions of the compressible isentropic Navier-Stokes equations

Communications in Partial Differential Equations

Volumn 22, Issue 5-6, 1997, Pages 977-1008

  Desjardins, Benoît ^a,b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002475403     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309708821291     Document Type: Article

References (20)

1. R. Coifman, P.L. Lions, Y. Meyer, S. Semmes, Compensated-compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), p.247-286.
2. B. Desjardins, A few remarks on ordinary differential equations, to appear in C.P.D.E..
3. B. Desjardins, Linear transport equations with values in Sobolev spaces and application to the Navier-Stokes equations, to appear in Diff. and Int. Equ.
4. B. Desjardins, Global existence results for the incompressible density dependant Navier-Stokes equations in the whole space, to appear in Diff. and Int. Equ.
5. B. Desjardins, Regularity results for two dimensional viscous flows, to appear in Arch. for Rat. Mech. Anal.
6. R.J. Di Perna, P.L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989), p. 511-547.
7. R.J. Di Perna, P.L. Lions, in preparation see also in Séminaire, EDP 1988-1989, Ecole Polytechnique, Palaiseau, 1989.
8. D. Hoff, Construction of solutions for compressible isentropic Navier-Stokes equations in one space dimension with non smooth initial data, Proc. Roy. Soc. Edinburgh, A 103 (1986), p. 310-315.
9. D. Hoff, Global existence for ID compressible isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc., 303 (1987), p. 169-181.
10. D. Hoff, Global well-posedness of the Cauchy problem for nonisentropic gas dynamics with discontinuous data, J. Diff. Eq., 95 (1992), p.33-73.
11. A.Y. Kazhikov, Y.Y. Shelukhin, Unique global solution with respect to time of the initial boundary value problems for one dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), p. 273-282.
12. P.L. Lions, Existence globale pour les equations de Navier-Stokes compressibles isentropiques. C.R. Acad. Sci. Paris, 316 (1993), p. 1335-1340.
13. P.L. Lions, Compacité des solutions des équations de Navier-Stokes compressibles isentrepiques, C.R. Acad. Sci. Paris, 317 (1993),p. 115-120.
14. P.L. Lions, Mathematical Topics in Fluid Mechanics, in preparation.
15. A. Majda, Compressible fluid flows and systems of conservation laws in several variables, Appl. Math. Sci., 53, Springer, (1984).
16. D. Serre, Solutions faibles globales des equations de Navier-Stokes pour un fluide compressible, C.R. Acad. Sci. Paris, 303 (1986), p. 629-642.
17. D. Serre, Sur l'équation monodimensionnelle d'un fluide visqueux compressible et conducteur de chaleur, C.R. Acad. Sci. Paris, 303 (1986), p.703-706.
18. D. Serre, Variations de grande amplitude pour la densite d'un fluide visqueux compressible, Physica D 48 (1991), p.113-128.
19. V.A. Solonnikov, Solvability of the initial boundary value problem fpr the equation of a viscous compressible fluid, J. Sov. Math., 14 (1980), p.1120-1133.
20. 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), p. 259-296.