Asymptotic profile of solutions to the linearized compressible Navier-Stokes flow

Abstract

We consider the asymptotic behavior as time goes to infinity of the $L^2$-norm of the velocity of the linearized compressible Navier-Stokes equations in ${\mathbf{R}}^n$ ($n\ge 2$). As an application we shall study the optimality of the decay rate for the $L^2$-norm of the velocity by deriving the decay estimate from below as time goes to infinity.

arXiv comment17 pages