Steady Vortex Rings in a Uniform Flow and Rearrangements of a Function

We prove the existence of steady vortex rings of an ideal fluid in a uniform flow. We use an approach based on a variational principle for the vorticity. We show equally that the maximiser (which represents a quantity related to the vorticity) of a functional related to kinetic energy and the impuls...

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Bibliographic Details
Published in:Resultate der Mathematik 2020-03, Vol.75 (1), Article 23
Main Author: Rebah, D.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We prove the existence of steady vortex rings of an ideal fluid in a uniform flow. We use an approach based on a variational principle for the vorticity. We show equally that the maximiser (which represents a quantity related to the vorticity) of a functional related to kinetic energy and the impulse over a class of rearrangements of a prescribed function ζ 0 , is in fact a rearrangement of ζ 0 .
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-019-1148-y