Asymptotic Stability of Plasma Boundary Layers to the Euler--Poisson Equations with Fluid-Boundary Interaction

Abstract

In the present paper, we discuss the behavior of a boundary layer, called a sheath, arising in the plasma physics. We define the sheath by a monotone stationary solution to the Euler--Poisson equations 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 asymptotic stability of the sheath for both the nondegenerate and degenerate cases based on a weighted energy method. At the same time, we obtain convergence rates toward the stationary solution subject to the spatial decay rates of the initial perturbation.