Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A priori estimates for the free-boundary Euler equations with surface
  tension in three dimensions   We derive a priori estimates for the incompressible free-boundary Euler
equations with surface tension in three spatial dimensions. Working in
Lagrangian coordinates, we provide a priori estimates for the local existence
when the initial velocity, which is rotational, belongs to $H^3$ and the trace
of initial velocity on the free boundary to $H^{3.5}$, thus lowering the
requirement on the regularity of initial data in the Lagrangian setting. Our
methods are direct and involve three key elements: estimates for the pressure,
the boundary regularity provided by the mean curvature, and the Cauchy
invariance.

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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an