Stability of rarefaction waves for the two-species Vlasov–Poisson–Boltzmann system with soft potentials

Abstract

In this paper, we construct the global solutions near a local Maxwellian for the onedimensional two-species Vlasov-Poisson-Boltzmann system with soft potentials. The macroscopic components of this local Maxwellian are the approximate rarefaction wave solutions to the associated one-dimensional compressible Euler system. Then we prove the stability of the rarefaction waves for the two-species Vlasov-Poisson-Boltzmann system in the weighted function space. Moreover, some time decay rates of the disparity between two species and the electric field are obtained.