Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain
Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain
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DOI：
10.18910/12262
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发表时间：
2008-12
影响因子：
0.4
通讯作者：
Y. Kagei;Takumi Nukumizu
中科院分区：
文献类型：
--
作者：
Y. Kagei;Takumi Nukumizu
在速度场无滑移边界条件下，在R中的柱面区域上研究了可压缩N-S方程在给定常态附近解的渐近行为。建立了常态扰动下的L衰变估计。文中还证明了扰动的时间渐近前导部分由一个满足一维热方程的函数给出。证明是基于能量方法和相关线性化半群的渐近分析。
Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a given constant state is investigated on a cylindrical domain in R, under the no slip boundary condition for the velocity field. The L 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.