On the motion of a vortex ring with a sharply concentrated vorticity

We study an incompressible non-viscous fluid with axial symmetry without sw irl, in the case when the vorticity is supported in an annulus. It is well known that there exist particular initial data for which the Euler evolutio n reduces to a translation with a constant speed. In this paper we prove a similar property for anp initial condition in the limit situation in which the initial vorticity is sharply concentrated, Copyright (C) 2000 John Wile y & Sons, Ltd.