Effects of fluid-boundary interaction on the stability of boundary layers in plasma physics

Abstract

The present article addresses the asymptotic stability of stationary solutions to a system of the Euler-Poisson equations with an interaction between fluids and boundaries. The system describes motions of positive ions in a boundary layer called a sheath in a plasma flow, formed under the Bohm criterion, which requires the outflow velocity to exceed the ion acoustic velocity. In this model, charged particles accumulate as the plasma arrive at the boundary, which, at the same time affects fluid flows by changing the electric field over the entire domain through the change in the boundary condition. We show that the boundary layer is asymptotically stable under this fluid-boundary interactive setting.