@article{RCP25_1995__47__1_0,
author = {Golse, Fran\c cois},
title = {Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results},
journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
volume = {47},
year = {1995},
pages = {1-31},
language = {en},
url = {http://dml.mathdoc.fr/item/RCP25_1995__47__1_0}
}
Golse, François. Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 47 (1995) pp. 1-31. http://gdmltest.u-ga.fr/item/RCP25_1995__47__1_0/
[1] ; Mathematical Methods of Classical Mechanics ; Springer Verlag, New York (1978). | MR 690288 | Zbl 0386.70001
[2] , , ; Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles; C. R. Acad. Sci. 309, 727-732, (1989). | MR 1054287 | Zbl 0697.35111
[3] , , ; Fluid Dynamic Limits of Kinetic Equations I : Formal Derivations; J. of Stat. Phys. 63, 323-344, (1991). | MR 1115587 | Zbl 1151.35066
[4] , , ; Fluid Dynamic Limits of Kinetic Equations II: Convergence Proofs for the Boltzmann Equation; Comm. on Pure and Appl. Math. 46, 667-753, (1993). | MR 1213991 | Zbl 0817.76002
[5] , , ; Fluid Dynamic Limits of Discrete Velocity Kinetic Equations; in "Advances in Kinetic Theory and Continuum Mechanics", R. Gatignol and Subbaramayer ed., pp. 57-72, Proceedings Springer Verlag Berlin (1991). | MR 1087069
[6] , , , ; The Nonaccretive Radiative Transfer Equations: Global Existence Results and Rosseland Approximation; J. of Funct. Anal. 77, 434-460, (1988). | MR 933978 | Zbl 0655.35075
[7] , ; The Classical Incompressible Navier-Stokes Limit of the Boltzmann Equation; Math. Models and Methods in the Appl. Sciences 1, 235-257, (1991). | MR 1115292 | Zbl 0758.35060
[8] , , ; Density Variations in Weakly Compressible Flows; submitted to Phys. of Fluids, (1990). | Zbl 0756.76061
[9] ; The Fluid Dynamic Limit of the Boltzmann Equation; Comm. on Pure and Appl. Math. 33, 651-666, (1980). | MR 586416 | Zbl 0424.76060
[10] ; Ph.D. Thesis, University of Arizona, (1991).
[11] ; The Boltzmann Equation and its Applications; Springer Verlag, New York (1988). | MR 1313028 | Zbl 0646.76001
[12] , ; Navier-Stokes Equations; Chicago Lectures in Mathematics, The University of Chicago Press, Chicago (1988). | MR 972259 | Zbl 0687.35071
[13] , , ; Incompressible Navier-Stokes and Euler Limits of the Boltzmann Equation; Comm. on Pure and Appl. Math. 42, 1189-1214, (1990). | MR 1029125 | Zbl 0689.76024
[14] , ; On the Cauchy Problem for the Boltzmann Equation: Global Existence and Weak Stability Results; Annals of Math. 130, 321-366, (1990). | MR 1014927 | Zbl 0698.45010
[15] , ; Linear Operators, Part I: General Theory; Interscience Publishers, New York (1958). | MR 1009162 | Zbl 0084.10402
[16] ; Solutions globales du problème de Cauchy pour l'équation de Boltzmann (d'après R. J. DiPerna et P.-L. Lions); Séminaire Bourbaki 1987-88, Exp. 699; Astérisque 161-162, 257-281, (1988). | Numdam | Zbl 0704.76041
[17] , , , ; Regularity of the Moments of the Solution of a Transport Equation; J. of Funct. Anal. 76, 110-125, (1988). | MR 923047 | Zbl 0652.47031
[18] , , ; Un résultat de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale de l'opérateur de transport; CR. Acad. Sci. 301, 341-344, (1985). | MR 808622 | Zbl 0591.45007
[19] , ; Limite fluide de l'équation de Boltzmann des semi-conducteurs pour une statistique de Fermi-Dirac; submitted to Asymptotic Anal., (1991). | MR 1193108 | Zbl 0784.35084
[20] , , ; On the Fluid Dynamic Approximation to the Boltzmann Equation at the Level of the Navier-Stokes Equation; Commun. in Math. Phys. 70, 97-124, (1979). | MR 553964 | Zbl 0449.76053
[21] , ; Comm. on Pure and Appl. Math. 34 p. 481, (1981); | MR 615627 | Zbl 0476.76068
, and Comm. on Pure and Appl. Math. 35 p. 629, (1982) | MR 668409 | Zbl 0478.76091
[22] ; Sur le mouvement d'un fluide visqueux emplissant l'espace ; Acta Math. 63, 193-248, (1934). | JFM 60.0726.05 | MR 1555394
[23] ; Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod (Paris 1965). | Zbl 0189.40603
[24] ; Fluid Dynamic Limit of the Nonlinear Boltzmann Equation at the Level of the Compressible Euler Equation; Commun, in Math. Phys. 61, 119-168, (1978). | MR 503305 | Zbl 0381.76060
[25] ; Global Existence to the BGK Model of the Boltzmann Equation; J. Diff. Eq. 82, 191-205, (1989). | MR 1023307 | Zbl 0694.35134
[26] ; Résultat d'existence pour le modèle de BGK de la théorie cinétique des gaz en domaine borné et non borné; preprint, (1991).
[27] ; Formation of Singularities in 3D Compressible Fluids; Commun. in Math. Phys. 101, 475-485, (1985). | MR 815196 | Zbl 0606.76088
[28] : Conference at the IVth Workshop on Mathematical Aspects of Fluid and Plasma Dynamics; Kyoto (1991).
[29] : Asymptotic Theory of Flow of Rarefied Gas over a Smooth Boundary II; in "Rarefied Gas Dynamics", D. Dini ed., 737-749, Editrice Tecnico Scientifica, Pisa (1971).
[30] , : Steady Gas Flows past Bodies at Small Knudsen Numbers; Transport Theory and Stat. Phys. 16, 189-199, (1987). | Zbl 0622.76082
[31] , : A Remark Concerning the Chapman-Enskog Asymptotics; in L. Desvillettes, Thèse d'habilitation, preprint Ecole Normale Supérieure, D.M.I., (1994). | MR 1323184 | Zbl 0863.76071