Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence of free-energy solutions to the 2D
  Patlak--Keller--Segel--Navier--Stokes system with critical and subcritical
  mass   We consider a coupled Patlak-Keller-Segel-Navier-Stokes system in
$\mathbb{R}^2$ that describes the collective motion of cells and fluid flow,
where the cells are attracted by a chemical substance and transported by
ambient fluid velocity, and the fluid flow is forced by the friction induced by
the cells. The main result of the paper is to show the global existence of
free-energy solutions to the 2D Patlak-Keller-Segel-Navier-Stokes system with
critical and subcritical mass.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th