Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy
  Method   We consider an initial value problem for a quadratically nonlinear inviscid
Burgers-Hilbert equation that models the motion of vorticity discontinuities.
We use a modified energy method to prove the existence of small, smooth
solutions over cubically nonlinear time-scales.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int