Global Strong Solutions of the Vlasov–Poisson–Boltzmann System in Bounded Domains

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 framework with a novel nonlinear-normed energy estimate of a distribution function in some weighted W-1,W-p-spaces and C-2,C--estimates of the self-consistent electric potential. Moreover we prove an exponential convergence of the distribution function toward the global Maxwellian.