Decay properties of solutions to the linearized compressible Navier-Stokes equation around time-periodic parallel flow

MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」Decay estimates on solutions to the linearized compressible Navier-Stokes equation around time-periodic parallel flow are established. It is shown that if the Reynolds and Mach numbers are sufficiently small, solutions of the linearized problem decay in L2 norm as an n−1 dimensional heat kernel. Furthermore, it is proved 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