标题： 通道中高雷诺数下层流单调剪切流的稳定性 显示英文标题

标题： Stability of laminar monotone shear flows in a channel for high Reynolds number

摘要： 我们考虑在大雷诺数极限下二维通道$\mathbb{R} \times[-1,1]$中层流流动$U\in C^4([-1,1])$的稳定性。 假设$U$是严格单调的，但允许$U^{\prime\prime}$为零，我们得到，如果算子$$ {\mathcal K}_{\nu}=-\frac{d^2}{dx^2}+\frac{U^{\prime\prime}}{U-\nu} \,, $$对所有满足$U^{\prime\prime}(U^{-1}(\nu))=0$的$\nu\in\mathbb{R}$都是严格正的，那么当雷诺数足够大时，$U$是稳定的。 这一贡献主要通过允许长波扰动（但比雷诺数小得多）来推广了之前的结果。 显示英文摘要

摘要： We consider the stability of a laminar flow $U\in C^4([-1,1])$ in the two-dimensional channel $\mathbb{R} \times[-1,1]$ in the large Reynolds number limit. Assuming that $U$ is strictly monotone but allowing $U^{\prime\prime}$ to vanish, we obtain that if the operator $$ {\mathcal K}_{\nu}=-\frac{d^2}{dx^2}+\frac{U^{\prime\prime}}{U-\nu} \,, $$ is strictly positive for all $\nu\in\mathbb{R}$ for which $U^{\prime\prime}(U^{-1}(\nu))=0$,then $U$ is stable for sufficiently large Reynolds number. This contribution generalizes previous results mostly by allowing long wave perturbations (but much shorter than the Reynolds number).