This article is cited in 7 papers

Classification of Casimirs in 2D hydrodynamics

Anton Izosimov, Boris Khesin

Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada

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.

MSC: Primary 76M60; Secondary 76A02, 58B2

Language: English

DOI: 10.17323/1609-4514-2017-17-4-699-716

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