Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results
Recherche Coopérative sur Programme n°25 (1995)
- Volume: 47, page 1-31
Access Full Article
topHow to cite
topGolse, François. "Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results." Recherche Coopérative sur Programme n°25 47 (1995): 1-31. <http://eudml.org/doc/274991>.
@article{Golse1995,
author = {Golse, François},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {1-31},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results},
url = {http://eudml.org/doc/274991},
volume = {47},
year = {1995},
}
TY - JOUR
AU - Golse, François
TI - Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results
JO - Recherche Coopérative sur Programme n°25
PY - 1995
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 47
SP - 1
EP - 31
LA - eng
UR - http://eudml.org/doc/274991
ER -
References
top- [1] V. Arnold; Mathematical Methods of Classical Mechanics ; Springer Verlag, New York (1978). Zbl0386.70001MR690288
- [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). Zbl0697.35111MR1054287
- [3] C. Bardos, F. Golse, D. Levermore; Fluid Dynamic Limits of Kinetic Equations I : Formal Derivations; J. of Stat. Phys.63, 323-344, (1991). Zbl1151.35066MR1115587
- [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). Zbl0817.76002MR1213991
- [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). MR1087069
- [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). Zbl0655.35075MR933978
- [7] C. Bardos, S. Ukai; The Classical Incompressible Navier-Stokes Limit of the Boltzmann Equation; Math. Models and Methods in the Appl. Sciences1, 235-257, (1991). Zbl0758.35060MR1115292
- [8] B. Bayly, D. Levermore, T. Passot; Density Variations in Weakly Compressible Flows; submitted to Phys. of Fluids, (1990). Zbl0756.76061
- [9] R. Caflisch; The Fluid Dynamic Limit of the Boltzmann Equation; Comm. on Pure and Appl. Math.33, 651-666, (1980). Zbl0424.76060MR586416
- [10] M. Campini; Ph.D. Thesis, University of Arizona, (1991).
- [11] C. Cercignani; The Boltzmann Equation and its Applications; Springer Verlag, New York (1988). Zbl0646.76001MR1313028
- [12] P. Constantin, C. Foias; Navier-Stokes Equations; Chicago Lectures in Mathematics, The University of Chicago Press, Chicago (1988). Zbl0687.35071MR972259
- [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). Zbl0689.76024MR1029125
- [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). Zbl0698.45010MR1014927
- [15] N. Dunford, J. Schwartz; Linear Operators, Part I: General Theory; Interscience Publishers, New York (1958). Zbl0084.10402MR1009162
- [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; Astérisque161-162, 257-281, (1988). Zbl0704.76041
- [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). Zbl0652.47031MR923047
- [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). Zbl0591.45007MR808622
- [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). Zbl0784.35084MR1193108
- [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). Zbl0449.76053MR553964
- [21] S. Klainerman, A. Majda; Comm. on Pure and Appl. Math.34 p. 481, (1981); Zbl0476.76068MR615627
- S. Klainerman, A. Majda and Comm. on Pure and Appl. Math.35 p. 629, (1982) Zbl0478.76091MR668409
- [22] J. Leray; Sur le mouvement d'un fluide visqueux emplissant l'espace ; Acta Math.63, 193-248, (1934). MR1555394JFM60.0726.05
- [23] J.-L. Lions; Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod (Paris1965). Zbl0189.40603
- [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). Zbl0381.76060MR503305
- [25] B. Perthame; Global Existence to the BGK Model of the Boltzmann Equation; J. Diff. Eq.82, 191-205, (1989). Zbl0694.35134MR1023307
- [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). Zbl0606.76088MR815196
- [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). Zbl0622.76082
- [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). Zbl0863.76071MR1323184
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.