## JMI2010A-5 Decay estimates on solutions of the linearized compressible Navier-Stokes equation around a Poiseuille type flow (pp.39-56)

Author(s)： Yoshiyuki Kagei, Yu Nagafuchi and Takeshi Sudou

J. Math-for-Ind. **2A** (2010) 39-56.

- File： JMI2010A-5.pdf (285KB)

Abstract

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 $L^2$ 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.

Keyword(s). compressible Navier-Stokes equation, decay estimates, asymptotic behavior, Poiseuille type flow