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Vortex Layers of Small Thickness
Author(s) -
Caflisch R. E.,
Lombardo M. C.,
Sammartino M. M. L.
Publication year - 2020
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21897
Subject(s) - vorticity , vortex , mathematics , geodetic datum , euler's formula , mathematical analysis , vorticity equation , euler equations , center (category theory) , geometry , physics , mechanics , geodesy , geology , chemistry , crystallography
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.