Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global weak solutions to a 3-dimensional degenerate and singular
  chemotaxis-Navier--Stokes system with logistic source   This paper considers the degenerate and singular chemotaxis-Navier--Stokes
system with logistic term
  $n_t + u\cdot\nabla n =\Delta n^m - \chi\nabla\cdot(n\nabla c) + \kappa n
-\mu n^2$, $x \in \Omega,\ t>0$,
  $c_t + u\cdot\nabla c = \Delta c - nc$, $x \in \Omega,\ t>0$,
  $u_t + (u\cdot\nabla)u = \Delta u + \nabla P + n\nabla\Phi, \quad \nabla\cdot
u = 0$, $x \in \Omega,\ t>0$, where $\Omega\subset \mathbb{R}^3$ is a bounded
domain and $\chi,\kappa \ge 0$ and $m, \mu >0$. In the above system without
fluid environment Jin (J. Differential Equations, 2017) showed existence and
boundedness of global weak solutions. On the other hand, in the above system
with $m=1$, Lankeit (Math.\ Models Methods Appl. Sci., 2016) established global
existence of weak solutions. However, the above system with $m>0$ has not been
studied yet. The purpose of this talk is to establish global existence of weak
solutions in the chemotaxis-Navier--Stokes system with degenerate diffusion and
logistic term.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom