Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost sure existence of global weak solutions for super-critical
  Navier-Stokes equations   In this paper we show that after suitable data randomization there exists a
large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb
T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for
which global energy bounds are proved. As a consequence, we obtain almost sure
super-critical global weak solutions. We also show that in 2d these global weak
solutions are unique.

9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol