The geometry and analysis of the averaged Euler equations and a new diffeomorphism group

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dc.creatorMarsden, J. E.
dc.creatorRatiu, T. S.
dc.creatorShkoller, S.
dc.date1999-08-19
dc.date.accessioned2026-07-07T05:30:24Z
dc.date.available2026-07-07T05:30:24Z
dc.descriptionWe present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of ${\mathbb R}^n$, this system of PDEs with Dirichlet boundary conditions are well-posed for initial data in the Hilbert space $H^s$, $s>n/2+1$. We then use a nonlinear Trotter product formula to prove that solutions of the averaged Euler equations are a regular limit of solutions to the averaged Navier-Stokes equations in the limit of zero viscosity. This system of PDEs is also the model for second-grade non-Newtonian fluids.
dc.identifierhttps://arxiv.org/abs/math/9908103
dc.identifierhttp://arxiv.org/abs/math/9908103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78981
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject58B20; 58D05; 76E99
dc.titleThe geometry and analysis of the averaged Euler equations and a new diffeomorphism group
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