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March 2008 Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer
Y. Kagei
Hiroshima Math. J. 38(1): 95-124 (March 2008). DOI: 10.32917/hmj/1207580346

Abstract

Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer ${\bf R}^{n-1}\times (0,a)$, $n\geq2$, under the no slip boundary condition for the velocity. The $L^p$ decay estimates of the solution are established for all $1\leq p\leq \infty$. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the $n-1$ dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup

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Y. Kagei. "Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer." Hiroshima Math. J. 38 (1) 95 - 124, March 2008. https://doi.org/10.32917/hmj/1207580346

Information

Published: March 2008
First available in Project Euclid: 7 April 2008

zbMATH: 1151.35072
MathSciNet: MR2397381
Digital Object Identifier: 10.32917/hmj/1207580346

Subjects:
Primary: 35Q30, 76N15

Rights: Copyright © 2008 Hiroshima University, Mathematics Program

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Vol.38 • No. 1 • March 2008
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