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  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.
|Original language||English (US)|
|Journal||Communications on Pure and Applied Mathematics|
|State||Accepted/In press - 2023|
ASJC Scopus subject areas
- Applied Mathematics