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

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dc.creatorGay-Balmaz, François
dc.creatorRatiu, Tudor S.
dc.date2005-04-19
dc.date.accessioned2026-07-07T05:19:14Z
dc.date.available2026-07-07T05:19:14Z
dc.descriptionThis 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.
dc.description35 pages
dc.identifierhttps://arxiv.org/abs/math/0504381
dc.identifierhttp://arxiv.org/abs/math/0504381
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74945
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject35Q35; 35Q53; 53D17; 53D22; 53D25; 58B20; 58B25; 58D05
dc.titleThe Lie-Poisson structure of the LAE-$α$ equation
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