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The resolvent problem of the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer $R^{n−1} × (0, a), n geqq 2$, under the no slip boundary co...ndition for the momentum. It is proved that the linearized operator is sectorial in $W^{1,p} × L^p for 1 < p < ∞$. The $L^p$ estimates for the resolvent are established for all $1 leqq p leqq ∞$. The estimates for the high frequency part of the resolvent are also derived, which lead to the exponential decay of the corresponding part of the semigroup.続きを見る
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Mendeley出力
layer-resolvent