Abstract
Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in $\mathbf{R}^{3}$, 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.
Citation
Yoshiyuki Kagei. Takumi Nukumizu. "Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain." Osaka J. Math. 45 (4) 987 - 1026, December 2008.
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