This website requires JavaScript.

On the stability of symmetric flows in a two-dimensional channel

Yaniv AlmogBernard Helffer
Dec 2022
摘要
We consider the stability of symmetric flows in a two-dimensional channel (including the Poiseuille flow). In 2015 Grenier, Guo, and Nguyen have established instability of these flows in a particular region of the parameter space, affirming formal asymptotics results from the 1940's. We prove that these flows are stable outside this region in parameter space. More precisely we show that the Orr-Sommerfeld operator $$ {\mathcal B}=\Big(-\frac{d^2}{dx^2}+i\beta(U+i\lambda)\Big)\Big(\frac{d^2}{dx^2}-\alpha^2\Big)-i\beta U^{\prime\prime}\,, $$ which is defined on $$ D({\mathcal B})=\{u\in H^4(0,1)\,,\, u^\prime(0)=u^{(3)}(0)=0 \mbox{ and }\,u(1)=u^\prime(1)=0\}. $$ is bounded on the half-plane $\Re \lambda \geq 0$ for$\alpha \gg \beta^{-1/10}$ or $\alpha \ll \beta^{-1/6}$.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答