Loss of Smoothness and Inherent Instability of 2D Inviscid Fluid Flows

The paper is focused on the loss of smoothness hypothesis which claims that vorticity (or vorticity gradients in the 2D case) grows unboundedly for the substantial part of the inviscid incompressible flows. At least, every steady flow is supposed to belong to the closure of this set (relative to a reasonably strong topology). We approach the problem involving both direct Lyapunov method and some sort of the linearization. We present new (and rather wide) classes of 2D flows in a generic domains which admit the loss of smoothness and related phenomena.