Global compressible Euler-Poisson limit of the ionic Vlasov-Poisson-Boltzmann system for all cutoff potentials

TL;DR

This paper proves that solutions of the ionic Vlasov-Poisson-Boltzmann system converge globally over time to solutions of the compressible ionic Euler-Poisson system across all cutoff potentials, using a novel analytical framework.

Contribution

It introduces a new weighted $H^1_{x,v}$-$W^{1, abla}_{x,v}$ framework and employs a truncated Hilbert expansion to establish the global convergence result.

Findings

Global convergence of solutions for all cutoff potentials

Development of a new weighted functional framework

Proof of smooth solution existence for the limit system

Abstract

The ionic Vlasov-Poisson-Boltzmann system is a fundamental model in dilute collisional plasmas. In this work, we study the compressible ionic Euler-Poisson limit of the ionic Vlasov-Poisson-Boltzmann system for the full range of cutoff potentials $-3 < \gamma \leq 1$. By employing a truncated Hilbert expansion together with a novel weighted $H^1_{x,v}$-$W^{1,\infty}_{x,v}$ framework, we prove that the solution of the ionic Vlasov-Poisson-Boltzmann converges globally in time to the smooth global solution of the compressible ionic Euler-Poisson system.