The Lie-Poisson structure of the LAE-$\alpha$ equation
Differential Geometry
2007-05-23 v1 Analysis of PDEs
Abstract
This paper shows that the time 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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Cite
@article{arxiv.math/0504381,
title = {The Lie-Poisson structure of the LAE-$\alpha$ equation},
author = {François Gay-Balmaz and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:math/0504381},
year = {2007}
}
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35 pages