Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local well-posedness for the motion of a compressible, self-gravitating
  liquid with free surface boundary   We establish the local well-posedness for the free boundary problem for the
compressible Euler equations describing the motion of liquid under the
influence of Newtonian self-gravity. We do this by solving a
tangentially-smoothed version of Euler's equations in Lagrangian coordinates
which satisfies uniform energy estimates as the smoothing parameter goes to
zero. The main technical tools are delicate energy estimates and optimal
elliptic estimates in terms of boundary regularity, for the Dirichlet problem
and Green's function.

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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin