Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blowup for $C^{2}$ Solutions of the N-dimensional Euler-Poisson
  Equations in Newtonian Cosmology   Pressureless Euler-Poisson equations with attractive forces are standard
models in Newtonian cosmology. In this article, we further develop the spectral
dynamics method and apply a novel spectral-dynamics-integration method to study
the blowup conditions for $C^{2}$ solutions with a bounded domain, $\left\Vert
X(t)\right\Vert \leq X_{0}$, where $\left\Vert\cdot\right\Vert $ denotes the
volume and $X_{0}$ is a positive constant. In particular, we show that if the
cosmological constant $\Lambda<M/X_{0}$, with the total mass $M$, then the
non-trivial $C^{2}$ solutions in $R^{N}$ with the irrotational initial
condition blow up at a finite time.

34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
30
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: patt-sol