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 $-3 < γ\leq 1$. 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.