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

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 $-3<\gamma \le 1$. By employing a truncated Hilbert expansion together with a novel weighted $H_{x,v}^1$-$W_{x,v}^{1,\infty }$ 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.

34 pages