Asymptotic stability of boundary layer to the multi-dimensional isentropic Euler-Poisson equations arising in plasma physics

This paper is concerned with the initial-boundary value problem on the isentropic Euler-Poisson equations arising in plasma physics in the half space for the spatial dimension n=1,2,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, 2, 3$$\end{document}. By assuming that the velocity of the positive ion satisfies the Bohm criterion at the far field, we establish the global unique existence and the large time asymptotic stability of boundary layer (i.e., stationary solution) in some weighted Sobolev spaces by weighted energy method. Moreover, the time-decay rates are also obtained.