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MARIA CARMELA LOMBARDO

Vortex layers of small thickness

Abstract

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 which does not depend on \$epsilon\$. Moreover the motion of the center of the layer is well approximated by the Birkhoff-Rott equation.