Low Regularity Solutions for the Vlasov-Poisson-Landau/Boltzmann System

Abstract

In the paper, we are concerned with the nonlinear Cauchy problem on the Vlasov-Poisson-Landau/Boltzmann system around global Maxwellians in torus or finite channel. The main goal is to establish the global existence and large time behavior of small amplitude solutions for a class of low regularity initial data. The molecular interaction type is restricted to the case of hard potentials for two classical collision operators because of the effect of the self-consistent forces. The result extends the one by Duan-Liu-Sakamoto-Strain [{\it Comm. Pure Appl. Math.} 74 (2021), no.~5, 932--1020] for the pure Landau/Boltzmann equation to the case of the VPL and VPB systems.