Linear stability of the Couette flow in the 3D isentropic compressible Navier-Stokes equations

Abstract

Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on $\mathbb{T}\times \mathbb{R}\times \mathbb{T}$. We prove the enhanced dissipation phenomenon for the linearized isentropic compressible Navier-Stokes equations around the Couette flow $(y,0,0{)}^{\top }$. Moreover, the lift-up phenomenon is also shown in this paper. Compared with the 3D incompressible Navier-Stokes equations [Ann. of Math.,185(2017), 541--608], the lift-up effect here is stronger due to the loss of the incompressible condition.

References in corpus (2)

• Transition threshold for the 3D Couette flow in a finite channel
• Linear stability analysis for 2D shear flows near Couette in the isentropic Compressible Euler equations

Cited by in corpus (1)

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