Bounds on the dispersion of vorticity in 2D incompressible, inviscid flowswith a priori unbounded velocity

We consider approximate solution sequences of the 2D incompressible Euler e quations obtained by mollifying compactly supported initial vorticities in L-p, 1 less than or equal to p less than or equal to 2, or bounded measures in H-loc(-1) and exactly solving the equations. For these solution sequenc es we obtain uniform estimates on the evolution of the mass of vorticity an d on the measure of the support of vorticity outside a ball of radius R. If the initial vorticity is in L-p, 1 less than or equal to p less than or eq ual to 2, these uniform estimates imply certain a priori estimates for weak solutions which are weak limits of these approximations. In the case of no nnegative vorticities, we obtain results that extend, in a natural way, the cubic-root growth of the diameter of the support of vorticity proved first by C. Marchioro for bounded initial vorticities [Comm. Math. Phys., 164 (1 994), pp. 507-524] and extended by two of the authors to initial vorticitie s in L-p, p > 2.