On decay properties of the linearized compressible Navier-Stokes equations around time-periodic flows in an infinite layer

摘要

We investigate decay properties of solutions to the linearized compressible Navier-Stokes equation around time-periodic parallel flow. We show that if the Reynolds and Mach numbers are sufficiently small, solutions of the linearized problem decay in L@~2 norm as an n - 1 dimensional heat kernel. Furthermore, we prove that the asymptotic leading part of solutions is given by solutions of an n- 1 dimensional linear heat equation with a convective term multiplied by time-periodic function.