Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darcy's law as low Mach and homogenization limit of a compressible fluid
  in perforated domains   We consider the homogenization limit of the compressible barotropic
Navier-Stokes equations in a three-dimensional domain perforated by
periodically distributed identical particles. We study the regime of particle
sizes and distances such that the volume fraction of particles tends to zero
but their resistance density tends to infinity. Assuming that the Mach number
is increasing with a certain rate, the rescaled velocity and pressure of the
microscopic system converges to the solution of an effective equation which is
given by Darcy's law. The range of sizes of particles we consider are exactly
the same which lead to Darcy's law in the homogenization limit of
incompressible fluids. Unlike previous results for the Darcy regime we estimate
the deficit related to the pressure approximation via the Bogovski\u{{\i}}
operator This allows for more flexible estimates of the pressure in Lebesgue
and Sobolev spaces and allows to proof convergence results for all barotropic
exponents $\gamma> \frac32$.

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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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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: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas