Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Nonlinear Analysis of the Averaged Euler Equations   This paper develops the geometry and analysis of the averaged Euler equations
for ideal incompressible flow in domains in Euclidean space and on Riemannian
manifolds, possibly with boundary. The averaged Euler equations involve a
parameter $\alpha$; one interpretation is that they are obtained by ensemble
averaging the Euler equations in Lagrangian representation over rapid
fluctuations whose amplitudes are of order $\alpha$. The particle flows
associated with these equations are shown to be geodesics on a suitable group
of volume preserving diffeomorphisms, just as with the Euler equations
themselves (according to Arnold's theorem), but with respect to a right
invariant $H^1$ metric instead of the $L^2$ metric. The equations are also
equivalent to those for a certain second grade fluid. Additional properties of
the Euler equations, such as smoothness of the geodesic spray (the Ebin-Marsden
theorem) are also shown to hold. Using this nonlinear analysis framework, the
limit of zero viscosity for the corresponding viscous equations is shown to be
a regular limit, {\it even in the presence of boundaries}.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin