Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The finite time blow-up for the Euler-Poisson equations in $\Bbb R^n$   We prove the finite time blow-up for $C^1$ solutions to the Euler-Poisson
equations in $\Bbb R^n$, $n\geq 1$, with/without background density for initial
data satisfying suitable conditions. We also find a sufficient condition for
the initial data such that $C^3$ solution breaks down in finite time for the
compressible Euler equations for polytropic gas flows.

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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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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: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph