Boundary Driven Instabilities of Couette Flows

Abstract

In this article, we prove that the threshold of instability of the classical Couette flow in \(H^s\) for large s is \(\nu ^{1/2}\). The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width \(\nu ^{1/2}\) which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.