Long‐Time Instability of the Couette Flow in Low Gevrey Spaces-Reference-Cited by-同舟云学术

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

Published:2023-04-24 Issue:10 Volume:76 Page:2804-2887
ISSN:0010-3640
Container-title:Communications on Pure and Applied Mathematics
language:en
Short-container-title:Comm Pure Appl Math

Author:

Deng Yu¹,Masmoudi Nader²³

Affiliation:

1. Department of Mathematics University of Southern California 3620 S. Vermont Avenue Los Angeles CA 90089 U.S.A.

2. NYUAD Research Institute, New York University Abu Dhabi PO Box 129188 Abu Dhabi UAE

3. Courant Institute 251 Mercer Street New York NY 10012 U.S.A.

Abstract

AbstractWe 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. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

Publisher

Wiley

Subject

Applied Mathematics,General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.22092

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