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.

References in corpus (14)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Global Strong Solutions of the Boltzmann Equation without Angular Cut-off
• Decay and Continuity of Boltzmann Equation in Bounded Domains
• The Vlasov-Maxwell-Boltzmann System in The Whole Space
• Optimal Large-Time Behavior of the Vlasov-Maxwell-Boltzmann System in the Whole Space
• Regularity of the Boltzmann Equation in Convex Domains
• Global mild solutions of the Landau and non-cutoff Boltzmann equations
• The Vlasov-Poisson-Boltzmann system without angular cutoff
• The Vlasov-Poisson-Landau System in ${\mathbb{R}}_x^3$
• The Boltzmann equation with specular boundary condition in convex domains
• Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains
• Global well-posedness of the Boltzmann equation with large amplitude initial data
• The Landau equation with the specular reflection boundary condition
• The initial boundary value problem for the Boltzmann equation with soft potential