@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, Série 4, Tome 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] 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] A model for collision processes in gases, Phys. Rev. 94 (1954) 511. | Zbl
, , ,[3] Fluid dynamic limits of kinetic equations I. Formal derivations, J. Statis. Phys. 63 (1991) 323-344. | MR
, , ,[4] 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] Acoustic and Stokes limits for the Boltzmann equation, C. R. Acad. Sci. Paris 327 (3) (1998) 323-328. | MR | Zbl
, , ,[6] Kinetic Equations and Asymptotic Theory, Series in Applied Mathematics, 4, Gauthier-Villars, Paris, 2000. | MR | Zbl
, , ,[7] The fluid dynamic limit of the Boltzmann equation, Comm. Pure Appl. Math. 33 (1980) 651-666. | MR | Zbl
,[8] The Boltzmann Equation and its Applications, Springer-Verlag, New York, 1988. | MR | Zbl
,[9] The Mathematical Theory of Dilute Gases, Applied Mathematical Sciences, 106, Springer-Verlag, 1994. | MR | Zbl
, , ,[10] Estimations de Strichartz pour les équations de transport cinétique, C. R. Acad. Sci. Paris 322 (6) (1996) 535-540. | MR | Zbl
, ,[11] Incompressible Navier-Stokes and Euler limits of the Boltzmann equation, Comm. Pure Appl. Math. 42 (1990) 1189-1214. | MR | Zbl
, , ,[12] On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math. 130 (2) (1991) 321-366. | MR | Zbl
, ,[13] Stokes and Acoustic limits for the Boltzmann equation: convergence proofs, Comm. Pure Appl. Math. 55 (3) (2002) 336-393. | MR | Zbl
, ,[14] 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] Pseudo-differential energy estimates of singular perturbations, Comm. Pure Appl. Math. 50 (9) (1997) 821-865. | MR | Zbl
,[17] Course of Theoretical Physics, Vol. 6: Fluid Mechanics, Pergamon Press, Oxford, 1987. | MR | Zbl
, ,[18] Sur le mouvement d'un fluide visqueux emplissant l'espace, Acta Math. 63 (1934) 193-248. | JFM | MR
,[19] Une approche locale de la limite incompressible, C. R. Acad. Sci. Paris 329 (1999) 387-392. | MR | Zbl
, ,[20] From Boltzmann equations to Navier-Stokes equations I, Archive Rat. Mech. Anal. 158 (2001) 173-193. | MR | Zbl
, ,[21] 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] Global existence to the BGK model of Boltzmann equation, J. Differential Equations 82 (1989) 191-205. | MR | Zbl
,[23] Kinetic modeling of polyatomic gas mixture, Phys. A. 105 (1981) 147.
, ,[24] Lattice gases, large deviations, and the incompressible Navier-Stokes equations, Ann. of Math. (2) 148 (1) (1998) 51-108. | MR | Zbl
, ,[25] Fast singular limits of Hyperbolic PDEs, J. Differential Equations 114 (1994) 476-512. | MR | Zbl
,[26] Discrete time Navier-Stokes limit for the BGK Boltzmann equation, Comm. Partial Diff. Equations 27 (2002) 149-184. | MR | Zbl
,[27] Incompressible hydrodynamic limits for a kinetic model of waves-particles interaction, Asympt. Anal. 19 (2) (1999) 149-183. | MR | Zbl
,[28] 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
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