The stability of sheath to the nonisentropic Euler-Poisson system with fluid-boundary interaction

Abstract

In the present paper, we define the sheath by a monotone stationary solution to the nonisentropic Euler-Poisson system under a condition known as the Bohm criterion and consider a situation in which charged particles accumulate on the boundary due to the flux from the inner region. Under this fluid-boundary interactive setting, we prove the large time asymptotic stability of the sheath provided that the initial perturbation is sufficiently small in some weighted Sobolev spaces. Moreover, the convergence rate of the solution toward the sheath is obtained. The proof is based on the weighted energy method.