Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of weak solutions to the Navier-Stokes equations
  (III)-frequency overlapping   If $u$ is a Leray-Hopf solution to the Navier-Stokes equations with the
initial data in $ L^2(\mathbb{R}^3)$, then $u$ is regular.

14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th