Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial regularity of Solutions of Navier-Stokes equations   In this paper, we study the singular set of 3-dimensional Navier-Stokes
equations. Under the
condition$\frac{1}{R^{\frac{3s}{q}+2-s}}\int^{R^{2}}_{0}(\int_{B_{R}}|u|^{q}dx)^{\frac{s}{q}}ds
<C,$ for $(q,s)\in\{(2,5),(5,2)\},$ we use the backward uniqueness of parabolic
equations to show that the Hausdorff dimension of the singular set is less than
1.

10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess