The Vlasov-Poisson-Boltzmann system without angular cutoff

Abstract

This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular non-cutoff with $-3<\gamma <-2s$ and $1/2\le s<1$, where $\gamma$, $s$ are two parameters describing the kinetic and angular singularities, respectively. We establish the global existence and convergence rates of classical solutions to the Cauchy problem when initial data is near Maxwellians. This extends the results in \cite{DYZ-h, DYZ-s} for the cutoff kernel with $-2\le \gamma \le 1$ to the case $-3<\gamma <-2$ as long as the angular singularity exists instead and is strong enough, i.e., $s$ is close to 1. The proof is based on the time-weighted energy method building also upon the recent studies of the non cutoff Boltzmann equation in \cite{GR} and the Vlasov-Poisson-Landau system in \cite{Guo5}.

34 pages, to appear in Communications in Mathematical Physics

References in corpus (2)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• The Vlasov-Poisson-Landau System in ${\mathbb{R}}_x^3$

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• Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential
• On the Vlasov-Poisson-Boltzmann limit of the Vlasov-Maxwell-Boltzmann system
• Stability of the Superposition of a Viscous Contact Wave with two Rarefaction Waves to the bipolar Vlasov-Poisson-Boltzmann System
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