On Rigorous Derivation of the Enskog Kinetic Equation

Autor:	Gapyak, I. V., Gerasimenko, V. I.
Rok vydání:	2011
Předmět:	Mathematical Physics Condensed Matter - Statistical Mechanics Mathematics - Analysis of PDEs 35Q20 35Q82 47J35 82C05 82C40
Zdroj:	Kinet. Relat. Models 5 (3) (2012) 459-484
Druh dokumentu:	Working Paper
DOI:	10.3934/krm.2012.5.459
Popis:	We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear kinetic Enskog equation and its generalizations are justified. It is established that for initial states which are specified in terms of one-particle distribution functions the description of the evolution by the Cauchy problem of the BBGKY hierarchy and by the Cauchy problem of the generalized Enskog kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is an equivalent. For the initial-value problem of the generalized Enskog equation the existence theorem is proved in the space of integrable functions. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1107.5572 Zobrazit plný text záznamu View this record from Arxiv