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Mathematical analysis of variable density flows in porous media

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Abstract

We consider a simple model describing the motion of a two-component mixture through a porous medium. We discuss well posedness of the associated initial-boundary value problem, in particular, with respect to the choice of boundary and far-field conditions. The existence of global-in-time solutions is proved in the ideal case when the fluid occupies the whole physical space. Finally, similar results are obtained also for the boundary value problems in the simplified 1-D geometry.

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Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic

    Eduard Feireisl & Hana Petzeltová

  2. CNRS et Laboratoire de Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405, Orsay Cedex, France

    Danielle Hilhorst

  3. Institut für Mathematik, Universität Rostock, Ulmenstraße 69, Haus 3, 18055, Rostock, Germany

    Peter Takáč

Authors
  1. Eduard Feireisl
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  2. Danielle Hilhorst
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  3. Hana Petzeltová
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  4. Peter Takáč
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Corresponding author

Correspondence to Eduard Feireisl.

Additional information

Eduard Feireisl: The research of E.F. leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement 320078. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO: 67985840.

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Feireisl, E., Hilhorst, D., Petzeltová, H. et al. Mathematical analysis of variable density flows in porous media. J. Evol. Equ. 16, 1–19 (2016). https://doi.org/10.1007/s00028-015-0290-6

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  • DOI: https://doi.org/10.1007/s00028-015-0290-6

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