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

TL;DR

This paper proves the large-time stability and convergence rate of a sheath solution in the nonisentropic Euler-Poisson system with fluid-boundary interaction, using weighted energy methods.

Contribution

It establishes the asymptotic stability of the sheath under small perturbations in a nonisentropic Euler-Poisson model with boundary interactions, which is a novel analysis.

Findings

Proved large-time asymptotic stability of the sheath.

Derived the convergence rate toward the sheath.

Validated stability under small initial perturbations.

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.