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Homogenization and low Mach number limit of compressible Navier-Stokes equations in critically perforated domains (2104.05578v2)
Published 12 Apr 2021 in math.AP
Abstract: In this note, we consider the homogenization of the compressible Navier-Stokes equations in a periodically perforated domain in $\mathbb{R}3$. Assuming that the particle size scales like $\varepsilon3$, where $\varepsilon>0$ is their mutual distance, and that the Mach number decreases fast enough, we show that in the limit $\varepsilon\to 0$, the velocity and density converge to a solution of the incompressible Navier-Stokes equations with Brinkman term. We strongly follow the methods of H\"ofer, Kowalczik and Schwarzacher [arXiv:2007.09031], where they proved convergence to Darcy's law for the particle size scaling like $\varepsilon\alpha$ with $\alpha\in (1,3)$.