Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the breakdown of solutions to the incompressible Euler equations with
  free surface boundary   We prove a continuation critereon for incompressible liquids with free
surface boundary. We combine the energy estimates of Christodoulou and Lindblad
with an analog of the estimate due to Beale, Kato, and Majda for the gradient
of the velocity in terms of the vorticity, and use this to show solution can be
continued so long as the second fundamental form and injectivity radius of the
free boundary, the vorticity, and one derivative of the velocity on the free
boundary remain bounded, assuming that the Taylor sign condition holds.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat