Linear stability analysis of the Couette flow for the two dimensional Euler-Poisson system

This paper is concerned with the linear stability analysis for the Couette flow of the Euler-Poisson system for both ionic fluid and electronic fluid in the domain T × R . We establish upper and lower bounds of the linearized solutions of the Euler-Poisson system near Couette flow. In particular, inviscid damping for the solenoidal component of the velocity is obtained.