Stability of rarefaction wave for the two-fluid full compressible Navier–Stokes–Poisson system under large initial perturbation

Abstract

In this paper, we are concerned with the asymptotic behavior of the solution to the Cauchy problem for the one-dimensional two-fluid full (non-isentropic) compressible Navier–Stokes–Poisson system, which models the motion of viscous charged particles (ions and electrons) in plasmas. The rarefaction wave is shown to be time-asymptotically stable under large initial perturbation as long as the strength of the rarefaction wave is sufficiently small and the adiabatic exponent $\gamma$ is close to 1. The proof is based on a delicate energy method, and the key point is to derive the uniform bounds of the density functions.