Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of an asymptotic model for free boundary Darcy flow in
  porous media in the critical Sobolev space   We prove that the quadratic approximation of the capillarity-driven
free-boundary Darcy flow is well posed in $ \dot{H}^{3/2} $, and globally
well-posed if the initial datum is small in $ \dot{H}^{3/2} $.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio