Linear stability analysis of the Couette flow for the 2D 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 $\text{bb}T\times \text{bb}R$. We establish the upper and lower bounds of the linearized solutions of the Euler-Poisson system near Couette flow. In particular, the inviscid damping for the solenoidal component of the velocity is obtained.