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

We study an incompressible non‐viscous fluid with axial symmetry without swirl, 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 evolution reduces to a translation with a constant speed. In this paper we prove a similar property for any initial condition in the limit situation in which the initial vorticity is sharply concentrated. Copyright © 2000 John Wiley & Sons, Ltd.