Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the analyticity of periodic gravity water waves with integrable
  vorticity function   We prove that the streamlines and the profile of periodic gravity water waves
traveling over a flat bed with wavespeed which exceeds the horizontal velocity
of all fluid particles are real-analytic graphs if the vorticity function is
merely integrable.

20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat