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

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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.

Original languageEnglish (US)
Pages (from-to)2804-2887
JournalCommunications on Pure and Applied Mathematics
Volume76
Issue number10
DOIs
StatePublished - Oct 2023

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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