The Lie-Poisson structure of the LAE-$α$ equation

Details The Lie-Poisson structure of the LAE-$α$ equation The Lie-Poisson structure of the LAE-$α$ equation

2005-04-19

arxiv.org/abs/math/0504381v1

Mathematics

Differential Geometry

35 pages

Scientific paper

This paper shows that the time $t$ map of the averaged Euler equations, with Dirichlet, Neumann, and mixed boundary conditions is canonical relative to a Lie-Poisson bracket constructed via a non-smooth reduction for the corresponding diffeomorphism groups. It is also shown that the geodesic spray for Neumann and mixed boundary conditions is smooth, a result already known for Dirichlet boundary conditions.

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