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

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 L2-L∞ framework with a novel nonlinear-normed energy estimate of a distribution function in some weighted W1,p-spaces and C2,δ-estimates of the self-consistent electric potential. Moreover we prove an exponential convergence of the distribution function toward the global Maxwellian.