Vortex Layers of Small Thickness

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

doi:10.1002/cpa.21897

Vortex Layers of Small Thickness

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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/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 language	English (US)
Pages (from-to)	2104-2179
Number of pages	76
Journal	Communications on Pure and Applied Mathematics
Volume	73
Issue number	10
DOIs	https://doi.org/10.1002/cpa.21897
State	Published - Oct 1 2020

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1002/cpa.21897

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AB - 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.

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Vortex Layers of Small Thickness

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