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

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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.
35 pages

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Differential Geometry, Analysis of PDEs, 35Q35; 35Q53; 53D17; 53D22; 53D25; 58B20; 58B25; 58D05

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http://salesiana.dossiersoluciones.com/handle/123456789/74945

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504381
 http://arxiv.org/abs/math/0504381

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arXiv