Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results
Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 47 (1995), Exposé no. 1, 31 p. 
@article{RCP25_1995__47__1_0,
     author = {Golse, Fran\c{c}ois},
     title = {Incompressible {Hydrodynamic} {Limits} of the {Boltzmann} {Equation} : a {Survey} of {Mathematical} {Results}},
     journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
     note = {talk:1},
     pages = {1--31},
     publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur},
     volume = {47},
     year = {1995},
     language = {en},
     url = {http://archive.numdam.org/item/RCP25_1995__47__1_0/}
}
TY  - JOUR
AU  - Golse, François
TI  - Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results
JO  - Les rencontres physiciens-mathématiciens de Strasbourg -RCP25
N1  - talk:1
PY  - 1995
SP  - 1
EP  - 31
VL  - 47
PB  - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
UR  - http://archive.numdam.org/item/RCP25_1995__47__1_0/
LA  - en
ID  - RCP25_1995__47__1_0
ER  - 
%0 Journal Article
%A Golse, François
%T Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results
%J Les rencontres physiciens-mathématiciens de Strasbourg -RCP25
%Z talk:1
%D 1995
%P 1-31
%V 47
%I Institut de Recherche Mathématique Avancée - Université Louis Pasteur
%U http://archive.numdam.org/item/RCP25_1995__47__1_0/
%G en
%F 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), Exposé no. 1, 31 p. http://archive.numdam.org/item/RCP25_1995__47__1_0/

[1] V. Arnold; Mathematical Methods of Classical Mechanics ; Springer Verlag, New York (1978). | MR | Zbl

[2] C. Bardos, F. Golse, D. Levermore; Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles; C. R. Acad. Sci. 309, 727-732, (1989). | MR | Zbl

[3] C. Bardos, F. Golse, D. Levermore; Fluid Dynamic Limits of Kinetic Equations I : Formal Derivations; J. of Stat. Phys. 63, 323-344, (1991). | MR | Zbl

[4] C. Bardos, F. Golse, D. Levermore; Fluid Dynamic Limits of Kinetic Equations II: Convergence Proofs for the Boltzmann Equation; Comm. on Pure and Appl. Math. 46, 667-753, (1993). | MR | Zbl

[5] C. Bardos, F. Golse, D. Levermore; 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

[6] C. Bardos, F. Golse, B. Perthame, R. Sentis; The Nonaccretive Radiative Transfer Equations: Global Existence Results and Rosseland Approximation; J. of Funct. Anal. 77, 434-460, (1988). | MR | Zbl

[7] C. Bardos, S. Ukai; The Classical Incompressible Navier-Stokes Limit of the Boltzmann Equation; Math. Models and Methods in the Appl. Sciences 1, 235-257, (1991). | MR | Zbl

[8] B. Bayly, D. Levermore, T. Passot; Density Variations in Weakly Compressible Flows; submitted to Phys. of Fluids, (1990). | Zbl

[9] R. Caflisch; The Fluid Dynamic Limit of the Boltzmann Equation; Comm. on Pure and Appl. Math. 33, 651-666, (1980). | MR | Zbl

[10] M. Campini; Ph.D. Thesis, University of Arizona, (1991).

[11] C. Cercignani; The Boltzmann Equation and its Applications; Springer Verlag, New York (1988). | MR | Zbl

[12] P. Constantin, C. Foias; Navier-Stokes Equations; Chicago Lectures in Mathematics, The University of Chicago Press, Chicago (1988). | MR | Zbl

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

[14] R. Diperna, P.-L. Lions; On the Cauchy Problem for the Boltzmann Equation: Global Existence and Weak Stability Results; Annals of Math. 130, 321-366, (1990). | MR | Zbl

[15] N. Dunford, J. Schwartz; Linear Operators, Part I: General Theory; Interscience Publishers, New York (1958). | MR | Zbl

[16] P. Gérard; 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). | EuDML | Numdam | Zbl

[17] F. Golse, P.-L. Lions, B. Perthame, R. Sentis; Regularity of the Moments of the Solution of a Transport Equation; J. of Funct. Anal. 76, 110-125, (1988). | MR | Zbl

[18] 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 de l'opérateur de transport; CR. Acad. Sci. 301, 341-344, (1985). | MR | Zbl

[19] F. Golse, F. Poupaud; Limite fluide de l'équation de Boltzmann des semi-conducteurs pour une statistique de Fermi-Dirac; submitted to Asymptotic Anal., (1991). | MR | Zbl

[20] S. Kawashima, A. Matsumura, T. Nishida; 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 | Zbl

[21] S. Klainerman, A. Majda; Comm. on Pure and Appl. Math. 34 p. 481, (1981); | MR | Zbl

S. Klainerman, A. Majda and Comm. on Pure and Appl. Math. 35 p. 629, (1982) | MR | Zbl

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

[23] J.-L. Lions; Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod (Paris 1965). | Zbl

[24] T. Nishida; 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 | Zbl

[25] B. Perthame; Global Existence to the BGK Model of the Boltzmann Equation; J. Diff. Eq. 82, 191-205, (1989). | MR | Zbl

[26] E. Ringeisen; Résultat d'existence pour le modèle de BGK de la théorie cinétique des gaz en domaine borné et non borné; preprint, (1991).

[27] T. Sideris; Formation of Singularities in 3D Compressible Fluids; Commun. in Math. Phys. 101, 475-485, (1985). | MR | Zbl

[28] K. Asano: Conference at the IVth Workshop on Mathematical Aspects of Fluid and Plasma Dynamics; Kyoto (1991).

[29] Y. Sone: 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] Y. Sone, K. Aoki: Steady Gas Flows past Bodies at Small Knudsen Numbers; Transport Theory and Stat. Phys. 16, 189-199, (1987). | Zbl

[31] L. Desvillettes, F. Golse: A Remark Concerning the Chapman-Enskog Asymptotics; in L. Desvillettes, Thèse d'habilitation, preprint Ecole Normale Supérieure, D.M.I., (1994). | MR | Zbl