Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the absence of "splash" singularities in the case of two-fluid
  interfaces   We show that "splash" singularities cannot develop in the case of locally
smooth solutions of the two-fluid interface in two dimensions. More precisely,
we show that the scenario of formation of singularities discovered by
Castro-C\'{o}rdoba-Fefferman-Gancedo-G\'{o}mez-Serrano in the case of the water
waves system, in which the interface remains locally smooth but self-intersects
in finite time, is completely prevented in the case of two-fluid interfaces
with positive densities.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an