Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness in smooth function spaces for the moving-boundary 1-D
  compressible Euler equations in physical vacuum   The free-boundary compressible 1-D Euler equations with moving physical
vacuum boundary are a system of hyperbolic conservation laws which are both
characteristic and degenerate. The physical vacuum singularity (or
rate-of-degeneracy) requires the sound speed $c= \gamma \rho^{\gamma -1}$ to
scale as the square-root of the distance to the vacuum boundary, and has
attracted a great deal of attention in recent years. We establish the existence
of unique solutions to this system on a short time-interval, which are smooth
(in Sobolev spaces) all the way to the moving boundary. The proof is founded on
a new higher-order Hardy-type inequality in conjunction with an approximation
of the Euler equations consisting of a particular degenerate parabolic
regularization. Our regular solutions can be viewed as degenerate viscosity
solutions.

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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga