Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence for the confined Muskat problem   In this paper we show global existence of Lipschitz continuous solution for
the stable Muskat problem with finite depth (confined) and initial data
satisfying some smallness conditions relating the amplitude, the slope and the
depth. The cornerstone of the argument is that, for these \emph{small} initial
data, both the amplitude and the slope remain uniformly bounded for all
positive times. We notice that, for some of these solutions, the slope can grow
but it remains bounded. This is very different from the infinite deep case,
where the slope of the solutions satisfy a maximum principle. Our work
generalizes a previous result where the depth is infinite.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
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The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org