Linear stability of the Couette flow for the non-isentropic compressible fluid

Abstract

We are concerned with the linear stability of the Couette flow for the non-isentropic compressible Navier-Stokes equations with vanished shear viscosity in a domain $\mathbb{T}\times \mathbb{R}$. For a general initial data settled in Sobolev spaces, we obtain a Lyapunov type instability of the density, the temperature, the compressible part of the velocity field, and also obtain an inviscid damping for the incompressible part of the velocity field. Moreover, if the initial density, the initial temperature and the incompressible part of the initial velocity field satisfy some quality relation, we can prove the enhanced dissipation phenomenon for the velocity field.

15pages

References in corpus (4)

• Transition threshold for the 3D Couette flow in a finite channel
• Stability of Couette flow for 2D Boussinesq system with vertical dissipation
• Linear stability analysis for 2D shear flows near Couette in the isentropic Compressible Euler equations
• Linear stability of the Couette flow in the 3D isentropic compressible Navier-Stokes equations