Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rayleigh-Taylor breakdown for the Muskat problem with applications to
  water waves   The Muskat problem models the evolution of the interface given by two
different fluids in porous media. The Rayleigh-Taylor condition is natural to
reach the linear stability of the Muskat problem. We show that the
Rayleigh-Taylor condition may hold initially but break down in finite time. As
a consequence of the method used, we prove the existence of water waves
turning.

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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
18
The categories of this paper are: econ