Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence of solutions to a parabolic-elliptic chemotaxis system
  with critical degenerate di ffusion   This paper is devoted to the analysis of non-negative solutions for a
degenerate parabolic-elliptic Patlak-Keller-Segel system with critical
nonlinear diffusion in a bounded domain with homogeneous Neumann boundary
conditions. Our aim is to prove the existence of a global weak solution under a
smallness condition on the mass of the initial data, there by completing
previous results on nite blow-up for large masses. Under some higher regularity
condition on solutions, the uniqueness of solutions is proved by using a
classical duality technique.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph