Long time instability of the Couette flow in low Gevrey spaces
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.01246
 Bibcode:
 2018arXiv180301246D
 Keywords:

 Mathematics  Analysis of PDEs;
 35Q31;
 35Q35
 EPrint:
 72 pages