Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interface evolution: the Hele-Shaw and Muskat problems   We study the dynamics of the interface between two incompressible 2-D flows
where the evolution equation is obtained from Darcy's law. The free boundary is
given by the discontinuity among the densities and viscosities of the fluids.
This physical scenario is known as the two dimensional Muskat problem or the
two-phase Hele-Shaw flow. We prove local-existence in Sobolev spaces when,
initially, the difference of the gradients of the pressure in the normal
direction has the proper sign, an assumption which is also known as the
Rayleigh-Taylor condition.

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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin