Large time behavior of solutions to the compressible Navier–Stokes equations around a parallel flow in a cylindrical domain

Stability of parallel flow of the compressible Navier–Stokes equation in a cylindrical domain is studied. It is shown that if the Reynolds and Mach numbers are sufficiently small, then parallel flow is asymptotically stable and the asymptotic leading part of the disturbances is described by a one dimensional viscous Burgers equation.