Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A thin film approximation of the Muskat problem with gravity and
  capillary forces   Existence of nonnegative weak solutions is shown for a thin film
approximation of the Muskat problem with gravity and capillary forces taken
into account. The model describes the space-time evolution of the heights of
the two fluid layers and is a fully coupled system of two fourth order
degenerate parabolic equations. The existence proof relies on the fact that
this system can be viewed as a gradient flow for the 2-Wasserstein distance in
the space of probability measures with finite second moment.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex