Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large-time behavior of the weak solution to 3D Navier-Stokes equations   The weak solution to the Navier-Stokes equations in a bounded domain $D
\subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided
that it satisfies an additional requirement. This solution exists for all $t
\geq 0$. In a bounded domain $D$ the solution decays exponentially fast as
$t\to \infty$ if the force term decays at a suitable rate.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph