Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains

TL;DR

This paper establishes the existence and uniqueness of global solutions to the Vlasov-Poisson-Boltzmann system in convex bounded domains, accounting for boundary effects, and proves exponential convergence to equilibrium.

Contribution

It introduces a novel nonlinear-normed energy estimate framework for the system in convex domains with diffuse boundary conditions.

Findings

Existence and uniqueness of global solutions

Exponential convergence to Maxwellian equilibrium

Development of a new energy estimate method

Abstract

When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition. The construction is based on an $L^{2}$-$L^{\infty}$ framework with a novel \textit{nonlinear-normed energy estimate} of a distribution function in weighted $W^{1,p}$-spaces and a $C^{2,\delta}$-estimate of the self-consistent electric potential. Moreover we prove an exponential convergence of the distribution function toward the global Maxwellian.