Vortex Layers of Small Thickness

R. E. Caflisch, M. C. Lombardo, M. M.L. Sammartino

Research output: Contribution to journalArticlepeer-review


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/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.

Original languageEnglish (US)
Pages (from-to)2104-2179
Number of pages76
JournalCommunications on Pure and Applied Mathematics
Issue number10
StatePublished - Oct 1 2020

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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