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arXiv · 1702.01843

Classification of Casimirs in 2D hydrodynamics

Anton Izosimov·Boris Khesin
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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.

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Anton Izosimov, Boris Khesin. 2017-02-07. Classification of Casimirs in 2D hydrodynamics. https://arxiv.org/abs/1702.01843

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