Long time instability of the Couette flow in low Gevrey spaces
Analysis of PDEs
2018-03-06 v1
Abstract
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.
Cite
@article{arxiv.1803.01246,
title = {Long time instability of the Couette flow in low Gevrey spaces},
author = {Yu Deng and Nader Masmoudi},
journal= {arXiv preprint arXiv:1803.01246},
year = {2018}
}
Comments
72 pages