Long-Time Instability of the Couette Flow in Low Gevrey Spaces

被引：13

作者：

Deng, Yu ^{[1
]}

Masmoudi, Nader ^{[2
,3
]}

机构：

[1] Univ Southern Calif, Dept Math, 3620 S Vermont Ave, Los Angeles, CA 90089 USA

[2] New York Univ Abu Dhabi, NYUAD Res Inst, POB 129188, Abu Dhabi, U Arab Emirates

[3] Courant Inst, 251 Mercer St, New York, NY 10012 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2023年 / 76卷 / 10期

关键词：

GLOBAL-SOLUTIONS; STABILITY; SYSTEM; DISTURBANCES; DYNAMICS; WAVES;

D O I：

10.1002/cpa.22092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is completely nonlinear and is due to some energy cascade. (c) 2023 Wiley Periodicals LLC.

引用

页码：2804 / 2887

页数：84

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