INSTANTANEOUS GAP LOSS OF SOBOLEV REGULARITY FOR THE 2D INCOMPRESSIBLE EULER EQUATIONS

We construct solutions of the 2D incompressible Euler equations in R-2 x [0, infinity) ) such that initially the velocity is in the super-critical Sobolev space H-beta for 1 < beta <2, , but is not in H(beta' )for beta(') > 1 + (3-beta)(beta-1)/2-(beta-1)(2) for any t is an element of (0, infinity ) . These solutions are not in the Yudovich class, but they exist globally in time and they are unique in a determined family of classical solutions.