Decay estimates on solutions of the linearized compressible Navier-Stokes equation around a Poiseuille type 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」Theorem 3.2 of [1] in J. Math-for-Ind. 2A (2010), pp. 39-56, contains an error. We modify the assumption on the initial value in order that Theorem 3.2 holds true.Decay estimates on solutions to the linearized compressible Navier-Stokes equation around a Poiseuille type 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