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Moscow Mathematical Journal, 2017, Volume 17, Number 4, Pages 699–716
DOI: https://doi.org/10.17323/1609-4514-2017-17-4-699-716 (Mi mmj654) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Classification of Casimirs in 2D hydrodynamics

Anton Izosimov, Boris Khesin

Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada
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DOI: https://doi.org/10.17323/1609-4514-2017-17-4-699-716
Abstract: We describe a complete list of Casimirs for 2D Euler hydrodynamics on a surface without boundary: we define generalized enstrophies which, along with circulations, form a complete set of invariants for coadjoint orbits of area-preserving diffeomorphisms on a surface. We also outline a possible extension of main notions to the boundary case and formulate several open questions in that setting.
Key words and phrases: area-preserving diffeomorphisms, enstrophy, Casimir function, coadjoint orbit, vorticity, circulation, hydrodynamical Euler equation, Reeb graph, Morse function.
Bibliographic databases:
Document Type: Article
MSC: Primary 76M60; Secondary 76A02, 58B2
Language: English
Citation: Anton Izosimov, Boris Khesin, “Classification of Casimirs in 2D hydrodynamics”, Mosc. Math. J., 17:4 (2017), 699–716
Citation in format AMSBIB
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\by Anton~Izosimov, Boris~Khesin
\paper Classification of Casimirs in 2D hydrodynamics
\jour Mosc. Math.~J.
\yr 2017
\vol 17
\issue 4
\pages 699--716
\mathnet{http://mi.mathnet.ru/mmj654}
\crossref{https://doi.org/10.17323/1609-4514-2017-17-4-699-716}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000416897600007}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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