  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.
