Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-term behaviour in a chemotaxis-fluid system with logistic source   We consider the coupled chemotaxis Navier-Stokes model with logistic source
terms \[ n_t + u\cdot \nabla n = \Delta n - \chi \nabla \cdot (n \nabla c) +
\kappa n - \mu n^2\] \[ c_t + u\cdot \nabla c = \Delta c - nc\] \[ u_t +
(u\cdot \nabla)u = \Delta u +\nabla P + n\nabla \Phi + f, \quad\qquad \nabla
\cdot u=0 \] in a bounded, smooth domain $\Omega\subset \mathbb{R}^3$ under
homogeneous Neumann boundary conditions for $n$ and $c$ and homogeneous
Dirichlet boundary conditions for $u$ and with given functions $f\in
L^\infty(\Omega\times(0,\infty))$ satisfying certain decay conditions and
$\Phi\in C^{1+\beta}(\bar\Omega)$ for some $\beta\in(0,1)$.
  We construct weak solutions and prove that after some waiting time they
become smooth and finally converge to the semi-trivial steady state
$(\frac{\kappa}{\mu},0,0)$.
  Keywords: chemotaxis, Navier-Stokes, logistic source, boundedness, large-time
behaviour

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess