Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)569-605
Journal / PublicationCommunications in Mathematical Physics
Volume268
Issue number3
Publication statusPublished - Dec 2006

Abstract

The time evolution of the distribution function for the charged particles in a dilute gas is governed by the Vlasov-Poisson-Boltzmann system when the force is self-induced and its potential function satisfies the Poisson equation. In this paper, we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global Maxwellian. Moreover, the convergence rate in time to the global Maxwellian is also obtained through the energy method. The proof is based on the theory of compressible Navier-Stokes equations with forcing and the decomposition of the solutions to the Boltzmann equation with respect to the local Maxwellian introduced in [23] and elaborated in [31]. © Springer-Verlag 2006.