Linear Stability of the Couette Flow in the 3D Isentropic Compressible Navier--Stokes Equations
Linear Stability of the Couette Flow in the 3D Isentropic Compressible Navier--Stokes Equations
Consider the linear stability of the three dimensional (3D) 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. In particular, due to the …