Remarks on large time behavior of the $L^{2}$-norm of solutions to strongly damped wave equations

Abstract

We reconsider the asymptotic behavior as $t \to +\infty$ of the $L^{2}$-norm of solutions to strongly damped wave equations in ${\bf R}^{n}$ with weighted initial data in the $n=1,2$ dimensional case. As an application, we shall apply those results to the analysis of the linearized compressible Navier-Stokes equations in ${\bf R}^{3}$.