From the Boltzmann equations to the equations of incompressible fluid mechanics, I

Archive for Rational Mechanics and Analysis

Volumn 158, Issue 3, 2001, Pages 173-193

  Lions, P L ^a   Masmoudi, N ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035616508     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050100143     Document Type: Article

References (23)

1. C. BARDOS, F. GOLSE & C. D. LEVERMORE. Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation. Comm. Pure Appl. Math. 46, 667-753, 1993.
2. C. BARDOS, F. GOLSE & C. D. LEVERMORE. Acoustic and Stokes limits for the Boltzmann equation. C. R. Acad. Sci. Paris Sér. I Math. 327, 323-328, 1998.
3. C. BARDOS, F. GOLSE & D. LEVERMORE. Fluid dynamic limits of kinetic equations. I. Formal derivations. J. Statist. Phys. 63, 323-344, 1991.
4. C. CERCIGNANI. The Boltzmann equation and its applications. Springer-Verlag, New York, 1988.
5. C. CERCIGNANI, R. ILLNER & M. PULVIRENTI. The mathematical theory of dilute gases. Springer-Verlag, New York, 1994.
6. J.-Y. CHEMIN. Fluides parfaits incompressibles. Astérisque 230, 177, 1995.
7. B. DESJARDINS, E. GRENIER, P.-L. LIONS & N. MASMOUDI. Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. J. Math. Pures Appl. (9), 78, 461-471, 1999.
8. R. J. DIPERNA & P.-L. LIONS. On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. of Math. (2), 130, 321-366, 1989.
9. R. J. DIPERNA & P.-L. LIONS. Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98, 511-547, 1989.
10. R. J. DIPERNA & P.-L. LIONS. Global solutions of Boltzmann's equation and the entropy inequality. Arch. Rational Mech. Anal. 114, 47-55, 1991.
11. F. GOLSE, P.-L. LIONS, B. PERTHAME & R. SENTIS. Regularity of the moments of the solution of a transport equation. J. Funct. Anal. 76, 110-125, 1988.
12. F. GOLSE, B. PERTHAME & R. SENTIS. Un résultat de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale d'un opérateur de transport. C. R. Acad. Sci. Paris Sér. I Math. 301, 341-344, 1985.
13. F. GOLSE & L. SAINTRAYMOND. Personal communiacation.
14. J. LERAY. Etude de diverses équations intégrales nonlinéaires et de quelques problèmes que pose l'hydrodynamique. J. Math. Pures Appl. 12, 1-82, 1933.
15. J. LERAY. Essai sur les mouvements plans d'un liquide visqueux emplissant l'espace. Acta. Math. 63, 193-248, 1934.
16. J. LERAY. Essai sur les mouvements plans d'un liquide visqueux qui limitent des parois. J. Math. Pures Appl. 13, 331-418, 1934.
17. P.-L. LIONS. Compactness in Boltzmann's equation via Fourier integral operators and applications. I. J. Math. Kyoto Univ. 34, 391-427, 1994.
18. P.-L. LIONS. Compactness in Boltzmann's equation via Fourier integral operators and applications. II. J. Math. Kyoto Univ. 34, 429-461, 1994.
19. P.-L. LIONS. Compactness in Boltzmann's equation via Fourier integral operators and applications. III. J. Math. Kyoto Univ. 34, 539-584, 1994.
20. P.-L. LIONS. Mathematical topics in fluid mechanics. Vol. 1.The Clarendon Press Oxford University Press, New York, 1996. Incompressible models, Oxford Science Publications.
21. P.-L. LIONS. Mathematical topics in fluid mechanics. Vol. 2. The Clarendon Press Oxford University Press, New York, 1998. Compressible models, Oxford Science Publications.
22. P.-L. LIONS & N. MASMOUDI. Incompressible limit for a viscous compressible fluid. J. Math. Pures Appl. (9), 77, 585-627, 1998.
23. P.-L. LIONS & N. MASMOUDI. Une approche locale de la limite incompressible. C. R. Acad. Sci. Paris Sér. I Math. 329, 387-392, 1999.