Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some sharper boundedness conditions in the higher-dimensional
  chemotaxis-consumption model   For the classical zero-flux chemotaxis-consumption model \begin{equation*}
u_t= \Delta u - \chi \nabla \cdot (u \nabla v) \quad \textrm{and}\quad
v_t=\Delta v- uv, \quad \text{ with } (x,t)\in \Omega \times (0,T_{max}),
\end{equation*} $\Omega$ being a bounded and smooth domain of $\mathbb{R}^n$,
$n\geq 3$, $\chi$ some positive number and $T_{max} \in (0,\infty]$, the
following was established in a paper by Tao: for every sufficiently regular
initial data $u(x,0)=u_0(x)\geq 0$ and $v(x,0)=v_0(x) \geq 0$, there is
$\chi(\lVert v_0 \rVert_{L^\infty(\Omega)})$ such that for all $0<\chi\leq
\chi(\lVert v_0 \rVert_{L^\infty(\Omega)})$, the initial-boundary value problem
has a unique classical solution in $\Omega \times (0,\infty)$ which is bounded.
In this paper, whenever $n\geq 5$, we obtain the same claim for larger values
of the constant $\chi(\|v_0\|_{L^{\infty}(\Omega)})$.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph