Dynamics of symplectic fluids and point vortices

Details Dynamics of symplectic fluids and point vortices Dynamics of symplectic fluids and point vortices

2011-06-08

arxiv.org/abs/1106.1609v1

Mathematics

Symplectic Geometry

12 pages

Scientific paper

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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