Dynamics of symplectic fluids and point vortices
Symplectic Geometry
2011-06-09 v1 Dynamical Systems
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 D.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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Cite
@article{arxiv.1106.1609,
title = {Dynamics of symplectic fluids and point vortices},
author = {Boris Khesin},
journal= {arXiv preprint arXiv:1106.1609},
year = {2011}
}
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12 pages