Global regularity for a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the 2D Euler equations

We present an a-regularization of the Birkhoff-Rott equation, induced by the two-dimensional Euler-a equations, for the vortex sheet dynamics. We show that an initially smooth self-avoiding vortex sheet remains smooth for all times under the a-regularized dynamics, provided the initial density of vorticity is an integrable function over the curve with respect to the arc-length measure. (C) 2008 Elsevier B.V. All rights reserved.