Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational Collapse for Polytropic Gaseous Stars: Self-similar
  Solutions   In the supercritical range of the polytropic indices $\gamma\in(1,\frac43)$
we show the existence of smooth radially symmetric self-similar solutions to
the gravitational Euler-Poisson system. These solutions exhibit gravitational
collapse in the sense that the density blows-up in finite time. Some of these
solutions were numerically found by Yahil in 1983 and they can be thought of as
polytropic analogues of the Larson-Penston collapsing solutions in the
isothermal case $\gamma=1$. They each contain a sonic point, which leads to
numerous mathematical difficulties in the existence proof.

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The categories of this paper are: adap-org
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th