Homogenization and low Mach number limit of compressible Navier-Stokes equations in critically perforated domains (Q2154515)

In this short note, the authors contribute with new results on the homogenization of compressible Navier-Stokes equations. Their focus is exclusively on unbounded domains that are periodically perforated with balls of critical size (i.e. the diameter of the typical inclusion \(\sim \epsilon^3\)). After handling suitably the inherently present boundary layers, they recover the classical Brinkman term in the upscaled limit equations. The employed working techniques are to a large extent similar to those used recently by \textit{R. M. Höfer} et al. [Math. Models Methods Appl. Sci. 31, No. 9, 1787--1819 (2021; Zbl 1480.35016)] when handling homogenization aspects of compressible Navier-Stokes equations, that leads to a Darcy term in the upscaled limit.