Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of global solutions for a Keller-Segel-fluid equations with
  nonlinear diffusion   We consider a coupled system consisting of the Navier-Stokes equations and a
porous medium type of Keller-Segel system that model the motion of swimming
bacteria living in fluid and consuming oxygen. We establish the global-in-time
existence of weak solutions for the Cauchy problem of the system in dimension
three. In addition, if the Stokes system, instead Navier-Stokes system, is
considered for the fluid equation, we prove that bounded weak solutions exist
globally in time.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph