Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of Non-Local Navier-Stokes-Korteweg Equations for
  Compressible Liquid-Vapour Flow in Porous Media   We consider a nonlocal version of the quasi-static Navier-Stokes-Korteweg
equations with a non-monotone pressure law. This system governs the
low-Reynolds number dynamics of a compressible viscous fluid that may take
either a liquid or a vapour state. For a porous domain that is perforated by
cavities with diameter proportional to their mutual distance the homogenization
limit is analyzed. We extend the results for compressible one-phase flow with
polytropic pressure laws and prove that the effective motion is governed by a
nonlocal version of the Cahn-Hilliard equation. Crucial for the analysis is the
convolution-like structure of the nonlocal capillarity term that allows to
equip the system with a generalized convex free energy. Moreover, the
capillarity term accounts not only for the energetic interaction within the
fluid but also for the interaction with a solid wall boundary.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat