Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global classical solutions in chemotaxis(-Navier)-Stokes system with
  rotational flux term   The coupled chemotaxis fluid system \begin{equation} \left\{
\begin{array}{llc} \displaystyle n_t=\Delta n-\nabla\cdot(nS(x,n,c)\cdot\nabla
c)-u\cdot\nabla n, &(x,t)\in \Omega\times (0,T),\\ c_t=\Delta c-nc-u\cdot\nabla
c , &(x,t)\in\Omega\times (0,T),\\ u_t=\Delta u-\kappa(u\cdot\nabla)u+\nabla
P+n\nabla\phi , &(x,t)\in\Omega\times (0,T),\\ \nabla\cdot
u=0,&(x,t)\in\Omega\times (0,T), \end{array} \right.(\star) \end{equation} is
considered under the no-flux boundary conditions for $n,c$ and the Dirichlet
boundary condition for $u$ on a bounded smooth domain
$\Omega\subset\mathbb{R}^N$ ($N=2,3$), $\kappa=0,1$. We assume that $S(x,n,c)$
is a matrix-valued sensitivity under a mild assumption such that
$|S(x,n,c)|<S_0(c_0)$ with some non-decreasing function $S_0\in
C^2((0,\infty))$. It contrasts the related scalar sensitivity case that
$(\star)$ does not possess the natural {\em gradient-like} functional
structure. Associated estimates based on the natural functional seem no longer
available. In the present work, a global classical solution is constructed
under a smallness assumption on $\|c_0\|_{L^\infty(\Omega)}$ and moreover we
obtain boundedness and large time convergence for the solution, meaning that
small initial concentration of chemical forces stabilization.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess