Asymptotic Behavior of Solutions to the Compressible Navier-Stokes Equation Around a Time-Periodic Parallel Flow

The global in time existence of strong solutions to the compressible Navier-Stokes equation around time-periodic parallel flows in R, n ≥ 2, is established under smallness conditions on Reynolds number, Mach number and initial perturbations. Furthermore, it is proved for n = 2 that the asymptotic leading part of solutions is given by a solution of one-dimensional viscous Burgers equation multiplied by timeperiodic function. In the case n ≥ 3 the asymptotic leading part of solutions is given by a solution of n− 1-dimensional heat equation with convective term multiplied by time-periodic function. Mathematics Subject Classification