Asymptotic profile of solutions to the linearized compressible   Navier-Stokes flow
  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 ${\bf R}^{n}$ ($n \geq 2$). 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. 
Ruy Coimbra Charao and Ryo Ikehata
math.AP