Linear Stability Analysis of the Couette Flow for the Two Dimensional Non-Isentropic Euler-Poisson System

Authors

Xueke Pu School of mathematics and information science, Guangzhou University, Guangzhou, 510006, People's Republic of China https://orcid.org/0000-0001-9144-2792
Xulong Wu School of mathematics and information science, Guangzhou University, Guangzhou, 510006, People's Republic of China
Lian Yang School of mathematics and information science, Guangzhou University, Guangzhou, 510006, People's Republic of China

DOI:

https://doi.org/10.37256/cm.6520256651

Keywords:

non-isentropic Euler-Poisson equations, Couette flow, linear stability, inviscid damping

Abstract

In the present paper, we study the linear stability of perturbations around the Couette flow for a two dimensional compressible non-isentropic Euler-Poisson system in the domain . A Lyapunov type instability result for the density and the temperature is obtained, and in particular, the inviscid damping for the solenoidal component of the velocity field is proved.