Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The inverse of the divergence operator on perforated domains with
  applications to homogenization problems for the compressible Navier-Stokes
  system   We study the inverse of the divergence operator on a domain $\Omega \subset
R^3$ perforated by a system of tiny holes. We show that such inverse can be
constructed on the Lebesgue space $L^p(\Omega)$ for any $1< p < 3$, with a norm
independent of perforation, provided the holes are suitably small and their
mutual distance suitably large. Applications are given to problems arising in
homogenization of steady compressible fluid flows.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc