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

In this paper, we study the homogenization of 3D non-homogeneous incompressible Navier-Stokes system in perforated domains with holes of critical size. Under very mild assumptions concerning the shape of the obstacles and their mutual distance, we show that when epsilon -> 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon \rightarrow 0$$\end{document}, the velocity and density converge to a solution of the non-homogeneous incompressible Navier-Stokes system with a friction term of Brinkman type.