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

Abstract:

We 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 ...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
Geometric and Functional Analysis
Volume:
10
Issue:
3
Pages:
582-599
Publication date:
1999-08-19
ISSN:
1016-443X
URN:
uuid:89f3a6a5-565c-4a6d-8e59-ee2b1d2c66fa
Source identifiers:
404791
Local pid:
pubs:404791
Language:
English
Keywords:

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