Vortex layers of small thickness

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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.
Original languageEnglish
Pages (from-to)2104-2179
Number of pages76
JournalCommunications on Pure and Applied Mathematics
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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