Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Refinement of the Local Serrin--Type Regularity A refinement of the
  local Serrin--type regularity criterion for a suitable weak solution to the
  Navier--Stokes equations   We formulate a new criterion for regularity of a suitable weak solution v to
the Navier-Stokes equations at the space-time point (x_0,t_0). The criterion
imposes a Serrin-type integrability condition on v only in a backward
neighbourhood of (x_0,t_0), intersected with the exterior of a certain
space-time paraboloid with vertex at point (x_0,t_0). We make no special
assumptions on the solution in the interior of the paraboloid.

37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex