From the BGK model to the Navier-Stokes equations
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 36 (2003) no. 2, pp. 271-317.
@article{ASENS_2003_4_36_2_271_0,
     author = {Saint-Raymond, Laure},
     title = {From the {BGK} model to the {Navier-Stokes} equations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {271--317},
     publisher = {Elsevier},
     volume = {Ser. 4, 36},
     number = {2},
     year = {2003},
     doi = {10.1016/S0012-9593(03)00010-7},
     zbl = {1067.76078},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0012-9593(03)00010-7/}
}
TY  - JOUR
AU  - Saint-Raymond, Laure
TI  - From the BGK model to the Navier-Stokes equations
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2003
SP  - 271
EP  - 317
VL  - 36
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S0012-9593(03)00010-7/
DO  - 10.1016/S0012-9593(03)00010-7
LA  - en
ID  - ASENS_2003_4_36_2_271_0
ER  - 
%0 Journal Article
%A Saint-Raymond, Laure
%T From the BGK model to the Navier-Stokes equations
%J Annales scientifiques de l'École Normale Supérieure
%D 2003
%P 271-317
%V 36
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S0012-9593(03)00010-7/
%R 10.1016/S0012-9593(03)00010-7
%G en
%F ASENS_2003_4_36_2_271_0
Saint-Raymond, Laure. From the BGK model to the Navier-Stokes equations. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 36 (2003) no. 2, pp. 271-317. doi : 10.1016/S0012-9593(03)00010-7. http://www.numdam.org/articles/10.1016/S0012-9593(03)00010-7/

[1] Arnold A., Markowich P., Toscani G., Unterreiter A., On logarithmic Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. PDE 26 (2001) 43-100. | MR | Zbl

[2] Bhatnagar P., Gross E.P., Krook M., A model for collision processes in gases, Phys. Rev. 94 (1954) 511. | Zbl

[3] Bardos C., Golse F., Levermore C.D., Fluid dynamic limits of kinetic equations I. Formal derivations, J. Statis. Phys. 63 (1991) 323-344. | MR

[4] Bardos C., Golse F., Levermore C.D., Fluid dynamic limits of kinetic equations II. Convergence proofs for the Boltzmann equation, Comm. Pure Appl. Math. 46 (5) (1993) 667-753. | MR | Zbl

[5] Bardos C., Golse F., Levermore C.D., Acoustic and Stokes limits for the Boltzmann equation, C. R. Acad. Sci. Paris 327 (3) (1998) 323-328. | MR | Zbl

[6] Bouchut F., Golse F., Pulvirenti M., Kinetic Equations and Asymptotic Theory, Series in Applied Mathematics, 4, Gauthier-Villars, Paris, 2000. | MR | Zbl

[7] Caflisch R., The fluid dynamic limit of the Boltzmann equation, Comm. Pure Appl. Math. 33 (1980) 651-666. | MR | Zbl

[8] Cercignani C., The Boltzmann Equation and its Applications, Springer-Verlag, New York, 1988. | MR | Zbl

[9] Cercignani C., Illner R., Pulvirenti M., The Mathematical Theory of Dilute Gases, Applied Mathematical Sciences, 106, Springer-Verlag, 1994. | MR | Zbl

[10] Castella F., Perthame B., Estimations de Strichartz pour les équations de transport cinétique, C. R. Acad. Sci. Paris 322 (6) (1996) 535-540. | MR | Zbl

[11] Demasi A., Esposito R., Lebowitz J., Incompressible Navier-Stokes and Euler limits of the Boltzmann equation, Comm. Pure Appl. Math. 42 (1990) 1189-1214. | MR | Zbl

[12] Diperna R., Lions P., On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math. 130 (2) (1991) 321-366. | MR | Zbl

[13] Golse F., Levermore C.D., Stokes and Acoustic limits for the Boltzmann equation: convergence proofs, Comm. Pure Appl. Math. 55 (3) (2002) 336-393. | MR | Zbl

[14] Golse F., Lions P., Perthame B., Sentis R., Regularity of the moments of the solution of a transport equation, J. Funct. Anal. 76 (1988) 110-125. | MR | Zbl

[15] Golse F., Saint-Raymond L., The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels, Inventiones Math., to appear. | MR | Zbl

[16] Grenier E., Pseudo-differential energy estimates of singular perturbations, Comm. Pure Appl. Math. 50 (9) (1997) 821-865. | MR | Zbl

[17] Landau L., Lifshitz E., Course of Theoretical Physics, Vol. 6: Fluid Mechanics, Pergamon Press, Oxford, 1987. | MR | Zbl

[18] Leray J., Sur le mouvement d'un fluide visqueux emplissant l'espace, Acta Math. 63 (1934) 193-248. | JFM | MR

[19] Lions P., Masmoudi N., Une approche locale de la limite incompressible, C. R. Acad. Sci. Paris 329 (1999) 387-392. | MR | Zbl

[20] Lions P., Masmoudi N., From Boltzmann equations to Navier-Stokes equations I, Archive Rat. Mech. Anal. 158 (2001) 173-193. | MR | Zbl

[21] Nishida T., Fluid dynamic limit of the nonlinear Boltzmann equation at the level of the compressible Euler equation, Comm. Math. Phys. 61 (1978) 119-168. | MR | Zbl

[22] Perthame B., Global existence to the BGK model of Boltzmann equation, J. Differential Equations 82 (1989) 191-205. | MR | Zbl

[23] Philippi P., Brun R., Kinetic modeling of polyatomic gas mixture, Phys. A. 105 (1981) 147.

[24] Quastel J., Yau H.-T., Lattice gases, large deviations, and the incompressible Navier-Stokes equations, Ann. of Math. (2) 148 (1) (1998) 51-108. | MR | Zbl

[25] Schochet S., Fast singular limits of Hyperbolic PDEs, J. Differential Equations 114 (1994) 476-512. | MR | Zbl

[26] Saint-Raymond L., Discrete time Navier-Stokes limit for the BGK Boltzmann equation, Comm. Partial Diff. Equations 27 (2002) 149-184. | MR | Zbl

[27] Saint-Raymond L., Incompressible hydrodynamic limits for a kinetic model of waves-particles interaction, Asympt. Anal. 19 (2) (1999) 149-183. | MR | Zbl

[28] Toscani G., Villani C., Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation, Comm. Math. Phys. 203 (3) (1999) 667-706. | MR | Zbl

[29] Welander P., Ark. Phys. 7 (1954) 507. | MR | Zbl

Cited by Sources: