The Lie-Poisson Structure of the Euler Equations of an Ideal Fluid

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dc.creatorVasylkevych, Sergiy
dc.creatorMarsden, Jerrold E.
dc.date2007-11-30
dc.date.accessioned2026-07-07T08:46:23Z
dc.date.available2026-07-07T08:46:23Z
dc.descriptionThis paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in R^n (or a smooth compact n-manifold with boundary) is a Poisson map relative to the Lie-Poisson bracket associated with the group of volume preserving diffeomorphism group. This is interesting and nontrivial because in Eulerian representation, the time t maps need not be C^1 from the Sobolev class H^s to itself (where s > (n/2) + 1). The idea of how this difficulty is overcome is to exploit the fact that one does have smoothness in the Lagrangian representation and then carefully perform a Lie-Poisson reduction procedure.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/0711.4875
dc.identifierhttp://arxiv.org/abs/0711.4875
dc.identifierDynamics of PDE, Vol.2, No.4, 281-300, 2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143234
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject35Q35; 53D17; 53D22; 53D25; 58B20; 58B25; 58D05;76B99
dc.titleThe Lie-Poisson Structure of the Euler Equations of an Ideal Fluid
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