Journal of Mathematical Fluid Mechanics

, Volume 17, Issue 2, pp 381–392 | Cite as

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

  • Eduard Feireisl
  • Yong Lu


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.


Weak Solution Strong Convergence Uniform Estimate Homogenization Problem Stokes System 
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© Springer Basel 2015

Authors and Affiliations

  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  2. 2.Faculty of Mathematics and Physics, Mathematical InstituteCharles University in PraguePraha 8Czech Republic

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