Vortex Layers of Small Thickness |
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| Authors: | R. E. Caflisch M. C. Lombardo M. M. L. Sammartino |
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| Affiliation: | 1. Courant Institute, 251 Mercer Street, New York, N.Y, 10012-1185 USA;2. Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy;3. Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy |
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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/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. |
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