论文标题
在$ l^\ infty $ prandtl扩展的稳定性中
On the $L^\infty$ stability of Prandtl expansions in Gevrey class
论文作者
论文摘要
在本文中，我们证明了$ l^\ infty \ cap l^2 $剪切流类型扩展的稳定性为$ \ big（y（y/\sqrtνN），0 \ big）$在Gevrey类中的初始扰动中，$ u（y）$（y（y）$是单调和浓缩函数$ cofcectific cofcectifcific coffice coffice。为此，我们为线性化的Orr-Sommerfeld操作员开发了直接分辨率估计方法，而不是Grenier，Guo和Nguyen引入的瑞利式迭代方法。
In this paper, we prove the $L^\infty\cap L^2$ stability of Prandtl expansions of shear flow type as $\big(U(y/\sqrtν),0\big)$ for the initial perturbation in the Gevrey class, where $U(y)$ is a monotone and concave function and $ν$ is the viscosity coefficient. To this end, we develop the direct resolvent estimate method for the linearized Orr-Sommerfeld operator instead of the Rayleigh-Airy iteration method introduced by Grenier, Guo and Nguyen.
