Large Time Behavior of the Vlasov-Poisson-Boltzmann System

Abstract

The motion of dilute charged particles can be modeled by Vlasov-Poisson-Boltzmann system. We study the large time stability of the VPB system. To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate $O\left(t^{-\infty }\right)$, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005). The improvement of the present paper is the removal of condition on parameter $\lambda$ as in the work of Li (2008).