Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local-existence for the Inhomogeneous Muskat problem   In this work we study the evolution of the interface between two different
fluids in a porous media with two different permeabilities. We prove local
existence in Sobolev spaces, when the free boundary is given by the
discontinuity among the densities and viscosities of the fluids.

6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph