Homogenization of Non-homogeneous Incompressible Navier-Stokes System in Critically Perforated Domains

Abstract: In this paper, we study the homogenization of 3D non-homogeneous incompressible Navier-Stokes system in perforated domains with holes of critical size. The diameter of the holes is of size \epsilon^3, where \epsilon is a small parameter measuring the mutual distance between the holes. We show that when \epsilon tends to 0, the velocity and density converge to a solution of the non-homogeneous incompressible Navier-Stokes system with a friction term of Brinkman type.