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 $L^2$-$L^{\infty }$ 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.

The current version of manuscript is published in Archive for Rational Mechanics and Analysis: https://rdcu.be/buOgc

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• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• The Boltzmann equation with specular boundary condition in convex domains
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