Vortex layers of small thickness

We consider a 2D vorticity configuration where vorticity is highly concentrated around a curve and exponentially decaying away from it: the intensity of the vorticity is O(1/epsilon) on the curve while it decays on an O(epsilon) distance from the curve itself. We prove that, if the initial datum is of vortex-layer type, Euler solutions preserve this structure for a time that does not depend on epsilon. Moreover, the motion of the center of the layer is well approximated by the Birkhoff-Rott equation. (c) 2020 Wiley Periodicals, Inc.