On the trivial solutions for the rotating patch model

In this paper, we study the clockwise simply connected rotating patches for Euler equations. By using the moving plane method, we prove that Rankine vortices are the only solutions to this problem in the class of slightly convex domains. We discuss in the second part of the paper the case where the...

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Bibliographic Details
Published in:Journal of evolution equations 2015-12, Vol.15 (4), p.801-816
Main Author: Hmidi, Taoufik
Format: Article
Language:English
Subjects:
Analysis
Analysis of PDEs
Mathematics
Mathematics and Statistics
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Summary:In this paper, we study the clockwise simply connected rotating patches for Euler equations. By using the moving plane method, we prove that Rankine vortices are the only solutions to this problem in the class of slightly convex domains. We discuss in the second part of the paper the case where the angular velocity Ω = 1 2 , and we show without any geometric condition that the set of the V-states is trivial and reduced to the Rankine vortices.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-015-0281-7