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

Yunbai Cao, Chanwoo Kim, Donghyun Lee

Published 2017-10-10Version 1

When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the dynamics of particles. 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 $L^{2}$-$L^{\infty}$ framework with a new weighted $W^{1,p}$-estimate of distribution function and $C^{2}$-estimate of the self-consistent electric potential. Moreover we prove an exponential convergence of distribution function toward the global Maxwellian.