On Rigorous Derivation of the Enskog Kinetic Equation

Details On Rigorous Derivation of the Enskog Kinetic Equation On Rigorous Derivation of the Enskog Kinetic Equation

2011-07-27

arxiv.org/abs/1107.5572v2

Physics

Mathematical Physics

28 pages

Scientific paper

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.

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