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

Abstrakt

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.

Klíčová slova

• Stationary compressible Navier–Stokes equations
• Homogenization
• Domain with holes