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Homogenization of Stationary Navier–Stokes Equations in Domains with Tiny Holes

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Abstract

We consider the homogenization problem for the stationary compressible Navier–Stokes equations describing a steady flow of a compressible Newtonian fluid in a bounded three dimensional domain. We focus on the case where the domain is perforated with very tiny holes for which the diameters are much smaller than their mutual distances. We show that the homogenization process does not change the motion of the fluids: in the asymptotic limit, we obtain again the same system of equations. This coincides with similar results for the stationary Stokes and stationary incompressible Navier–Stokes system.

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Authors and Affiliations

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

    Eduard Feireisl

  2. Faculty of Mathematics and Physics, Mathematical Institute, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Eduard Feireisl & Yong Lu

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  1. Eduard Feireisl
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  2. Yong Lu
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Correspondence to Eduard Feireisl.

Additional information

Eduard Feireisl and Yong Lu acknowledges the support of the project LL1202 in the programme ERC-CZ funded by the Ministry of Education, Youth and Sports of the Czech Republic.

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Feireisl, E., Lu, Y. Homogenization of Stationary Navier–Stokes Equations in Domains with Tiny Holes. J. Math. Fluid Mech. 17, 381–392 (2015). https://doi.org/10.1007/s00021-015-0200-2

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  • DOI: https://doi.org/10.1007/s00021-015-0200-2

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