Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global in time existence of strong solution to 3D periodic Navier-Stokes
  equations   The purpose of this paper is to bring to light a method through which the
global in time existence for arbitrary large in $H^1$ initial data of a strong
solution to 3D periodic Navier-Stokes equations follows. The method consists of
subdividing the time interval of existence into smaller sub-intervals carefully
chosen. These sub-intervals are chosen based on the hypothesis that for any
wavenumber $m$, one can find an interval of time on which the energy quantized
in low-frequency components (up to $m$) of the solution $u$ is lesser than the
energy quantized in high-frequency components (down to $m$) or otherwise the
opposite. We associate then a suitable number $m$ to each one of the intervals
and we prove that the norm $\|u(t)\|_{H^1}$ is bounded in both mentioned cases.
The process can be continued until reaching the maximal time of existence
$T_{max}$ which yields the global in time existence of strong solution.

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat