Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An optimal result for global existence and boundedness in a
  three-dimensional Keller-Segel-Stokes system with nonlinear diffusion   This paper investigates the following quasilinear Keller-Segel-Navier-Stokes
system $$\left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta
n^m-\nabla\cdot(n\nabla c),\quad x\in \Omega, t>0, \\ c_t+u\cdot\nabla c=\Delta
c-c+n,\quad x\in \Omega, t>0,\\ u_t+\nabla P=\Delta u+n\nabla \phi,\quad x\in
\Omega, t>0,\\ \nabla\cdot u=0, \quad x\in \Omega, t>0 \end{array}\right.$$
under homogeneous boundary conditions of Neumann type for $n$ and $c$, and of
Dirichlet type for $u$ in a three-dimensional bounded domains $\Omega\subseteq
\mathbb{R}^3$ with smooth boundary, where $\phi\in W^{1,\infty}(\Omega),m>0$.
It is proved that if $m>\frac{4}{3}$, then for any sufficiently regular
nonnegative initial data there exists at least one global boundedness solution
for system $(KSF)$, which in view of the known results for the fluid-free
system mentioned below (see Introduction) is an optimal restriction on $m$.

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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin