Dual pairs in fluid dynamics

Details Dual pairs in fluid dynamics Dual pairs in fluid dynamics

2010-07-08

arxiv.org/abs/1007.1347v1

Mathematics

Symplectic Geometry

33 pages

Scientific paper

This paper is a rigorous study of the dual pair structure of the ideal fluid and the dual pair structure for the $n$-dimensional Camassa-Holm (EPDiff) equation, including the proofs of the necessary transitivity results. In the case of the ideal fluid, we show that a careful definition of the momentum maps leads naturally to central extensions of diffeomorphism groups such as the group of quantomorphisms and the Ismagilov central extension.

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