Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cheap Caffarelli-Kohn-Nirenberg inequality for Navier-Stokes equations
  with hyper-dissipation   We prove that for the Navier Stokes equation with dissipation
$(-\Delta)^{\alpha}$, where $1<\alpha<{5/4}$, and smooth initial data, the
Hausdorff dimension of the singular set at time of first blow up is at most
$5-4\alpha$. This unifies two directions from which one might approach the Clay
prize problem.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an