Vortex Layers of Small Thickness

Abstract

AbstractWe 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/ε) on the curve while it decays on an O(ε) 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 ε. Moreover, the motion of the center of the layer is well approximated by the Birkhoff‐Rott equation. © 2020 Wiley Periodicals, Inc.