Resolvent Estimates for the Linearized Compressible Navier-Stokes Equation in an Infinite Layer
Resolvent Estimates for the Linearized Compressible Navier-Stokes Equation in an Infinite Layer
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DOI：
10.1619/fesi.50.287
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发表时间：
2007-08
期刊：
影响因子：
--
通讯作者：
Y. Kagei
中科院分区：
文献类型：
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作者：
Y. Kagei
在动量无滑移边界条件下，考虑无限层 Rn-1 × (0,a), n ≥ 2 中围绕给定常数状态的线性化可压缩纳维-斯托克斯方程的求解问题。证明了线性化算子在 W1,p × Lp 上是扇形的，且 1 < p < ∞。针对所有 1 ≤ p ≤ ∞ 建立了解析的 Lp 估计值。还导出了解析式高频部分的估计，这导致半群相应部分的指数衰减。
The resolvent problem of the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 × (0,a), n ≥ 2, under the no slip boundary condition for the momentum. It is proved that the linearized operator is sectorial in W1,p × Lp for 1 < p < ∞. The Lp estimates for the resolvent are established for all 1 ≤ p ≤ ∞. 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.