ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE COMPRESSIBLE NAVIER-STOKES EQUATION IN A CYLINDRICAL DOMAIN

Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in R-3, under the no slip boundary condition for the velocity field. The L-2 decay estimate is established for the perturbation from the constant state. It is also shown that the time-asymptotic leading part of the perturbation is given by a function satisfying a 1 dimensional heat equation. The proof is based on an energy method and asymptotic analysis for the associated linearized semigroup.