Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak entropy solution for a Keller-Segel type fluid model   In this paper, we consider a Keller-Segel type fluid model, which is a kind
of Euler-Poisson system with a self-gravitational force. We show that similar
to the parabolic case, there is a critical mass $8\pi$ such that if the initial
total mass $M$ is supercritical, i.e., $M> 8\pi$, then any weak entropy
solution with the same mass $M$ must blow up in finite time. The a priori
estimates of weak entropy solutions for critical mass $M=8\pi$ and subcritical
mass $M<8\pi$ are also obtained.

7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph