Abstract:
I show that the 2D Euler equations, when linearized around self-similar states near Couette flow, contain the full nonlinear resonance cascade mechanism, yielding Gevrey 2 as a critical regularity class. Moreover, there exists a Gevrey regular class of initial data, for which the velocity asymptotically converges in L2 but for which the vorticity diverges to infinity in Sobolev regularity. Thus, on the one hand, the physical phenomenon of inviscid damping holds. On the other, "strong damping" cannot hold due to blow-up. This is joint work with Yu Deng (USC).