Stability of contact discontinuity for the two-species Vlasov–Poisson–Boltzmann system

Abstract

This paper is devoted to the study of the nonlinear stability of contact wave for the Vlasov–Poisson–Boltzmann system with two-species. Based on the quasi-neutral Euler system in Lagrangian coordinates, we first construct a nontrivial profile: a local bi-Maxwellian whose parameters are also called “viscous contact wave” in the sense of hydrodynamics, then we prove that such a nontrivial profile is time-asymptotically stable by a refined energy method. For the proof, the good structure of the macroscopic equations is fruitfully exploited to attain the dissipation of the specific volumes and the electric potential, moreover, both of Lagrangian and Eulerian coordinates transformation are alternatively utilized in order to capture the higher-order energy of the electric potential.