Boundary driven instabilities of Couette flows

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