Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Angled crested like water waves with surface tension: Wellposedness of
  the problem   We consider the capillary-gravity water wave equation in two dimensions. We
assume that the fluid is inviscid, incompressible, irrotational and the air
density is zero. We construct an energy functional and prove a local
wellposedness result without assuming the Taylor sign condition. When the
surface tension $\sigma$ is zero, the energy reduces to a lower order version
of the energy obtained by Kinsey and Wu [23] and allows angled crest
interfaces. For positive surface tension, the energy does not allow angled
crest interfaces but admits initial data with large curvature of the order of
$\sigma^{-\frac{1}{3} + \epsilon} $ for any $\epsilon >0$.

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The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat