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 L2 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.
|Number of pages||40|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - Dec 2008|
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