Vortex Layers of Small Thickness | Zendy

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

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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.

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