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Dynamics of symplectic fluids and point vortices

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Abstract

We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend Ebin’s long-time existence result for geodesics on the symplectomorphism group to metrics not necessarily compatible with the symplectic structure. We also study the dynamics of symplectic point vortices, describe their symmetry groups and integrability.

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Authors and Affiliations

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

    Boris Khesin

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  1. Boris Khesin
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Correspondence to Boris Khesin.

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In memory of Vladimir Igorevich Arnold

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Khesin, B. Dynamics of symplectic fluids and point vortices. Geom. Funct. Anal. 22, 1444–1459 (2012). https://doi.org/10.1007/s00039-012-0182-7

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  • DOI: https://doi.org/10.1007/s00039-012-0182-7

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