Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the energy equality for weak solutions of the 3D Navier-Stokes
  equations   We prove that the energy equality holds for weak solutions of the 3D
Navier-Stokes equations in the functional class $L^3([0,T);V^{5/6})$, where
$V^{5/6}$ is the domain of the fractional power of the Stokes operator
$A^{5/12}$.

20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics