Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Logarithmic spikes of gradients and uniqueness of weak solutions to a
  class of active scalar equations
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg