数学
普朗特数
解决方案
索波列夫空间
数学分析
指数
纳维-斯托克斯方程组
类型(生物学)
理论(学习稳定性)
边界(拓扑)
操作员(生物学)
单调函数
有界函数
流量(数学)
压缩性
数学物理
几何学
物理
热力学
语言学
基因
计算机科学
机器学习
生物
哲学
抑制因子
化学
转录因子
传热
生态学
生物化学
作者
David Gérard-Varet,Yasunori Maekawa,Nader Masmoudi
标识
DOI:10.1215/00127094-2018-0020
摘要
We investigate the stability of boundary layer solutions of the two-dimensional incompressible Navier-Stokes equations. We consider shear flow solutions of Prandtl type : $$ u^\nu(t,x,y) \, = \, \big (U^E(t,y) + U^{BL}(t,\frac{y}{\sqrt{\nu}})\,, \, 0 \big )\, , \quad 0<\nu \ll 1\,. $$ We show that if $U^{BL}$ is monotonic and concave in $Y = y /\sqrt{\nu}$ then $u^\nu$ is stable over some time interval $(0,T)$, $T$ independent of $\nu$, under perturbations with Gevrey regularity in $x$ and Sobolev regularity in $y$. We improve in this way the classical stability results of Sammartino and Caflisch in analytic class (both in $x$ and $y$). Moreover, in the case where $U^{BL}$ is steady and strictly concave, our Gevrey exponent for stability is optimal. The proof relies on new and sharp resolvent estimates for the linearized Orr-Sommerfeld operator.
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