Boltzmann-grad limit for a particle system in continuum
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 6, p. 753-796
@article{AIHPB_1997__33_6_753_0,
     author = {Rezakhanlou, Fraydoun and Tarver, James E.},
     title = {Boltzmann-grad limit for a particle system in continuum},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {6},
     year = {1997},
     pages = {753-796},
     zbl = {0888.60076},
     mrnumber = {1484540},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1997__33_6_753_0}
}
Rezakhanlou, Fraydoun; Tarver, James E. Boltzmann-grad limit for a particle system in continuum. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 6, pp. 753-796. https://www.numdam.org/item/AIHPB_1997__33_6_753_0/

[1] D. Aldous, Stopping times and tightness, Annals of Probability, Vol. 6, 2, 1978, pp. 335-340. | MR 474446 | Zbl 0391.60007

[2] N. Bellomo and T. Gustafsson, The discrete Boltzmann equation: a review of the mathematical aspects of the initial and initial-boundary value problems, Reviews in Mathematical Physics, Vol. 3, 2, 1991, pp. 137-162. | MR 1121467 | Zbl 0737.76065

[3] J.-M. Bony, Solutions globales bornées pour les modèles discrets de l'équation de Boltzmann en dimension 1 d'espace, Journées Equations aux Dérivées Partielles, Saint-Jean-de-Monts, 1987. | Numdam

[4] S. Caprino and M. Pulvirenti, A cluster expansion approach to a one-dimensional Boltzmann equation: a validity result, in Communications in Mathematical Physics , Vol. 166, 3, 1995, pp. 603-631. | MR 1312437 | Zbl 0811.60099

[5] R. Gatignol, Théorie cinétique des gaz à répartition discrète de vitesses, Vol. 36 of Lecture Notes in Physics. Springer-Verlag, 1975. | MR 416379

[6] K. Hamdache, Existence globale et comportement asymptotique pour l'équation de Boltzmann à répartition discrète des vitesses, Journal de Mécanique Théorique et Appliquée, Vol. 3, 5, 1984, pp. 761-785. | MR 775789 | Zbl 0605.76091

[7] O. Lanford Iii, The evolution of large classical systems. In E. J. Moser, editor, Dynamical System, Theory and Applications, Vol. 38 of Lecture Notes in Physics, p. 1-111, Springer-Verlag, Berlin 1975. | MR 479206 | Zbl 0329.70011

[8] R. Illner and M. Pulvirenti, Gloval validity of the Boltzmann equation for a two- and three-dimensional rare gase in vacuum: erratum and improved result. Communications in Mathematical Physics, 121, 1989, pp. 143-146. | MR 985619 | Zbl 0850.76600

[9] R. Monaco and L. Preziosi, Fluid Dynamic Applications of the Discrete Boltzmann Equation. World Scientific, Singapore, 1991. | MR 1148366 | Zbl 0761.76001

[10] T. Platkowski and R. Illner, Discrete velocity models of the Boltzmann equation: a survey on the mathematical aspects of the theory, SIAM Review, Vol. 30, 2, 1988, pp. 213-255. | MR 941111 | Zbl 0668.76087

[11] M. Pulvirenti, Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum, Communications in Mathematical Physics, Vol. 113, 1987, pp. 79-85. | MR 918406 | Zbl 0665.76088

[12] F. Rezakhanlou, Kinetic limits for a class of interacting particle systems, Probability Theory and Related Fields, Vol. 104, 1, 1996, pp. 97-146. | MR 1367669 | Zbl 0838.60085

[13] L. Tartar, Existence globale pour un système hyperbolique semilinéaire de la théorie cinétique des gaz, Séminaire Goulaouic-Schwartz (1975/1976), 1976. | Numdam | Zbl 0336.35069

[14] L. Tartar, Some existence theorems for semilinear hyperbolic systems in one space variable. Technical report, Unisersity of Wisconsin-Madison, 1980.