Brinkman's law as $Γ$-limit of compressible low Mach Navier-Stokes equations and application to randomly perforated domains
We consider the time-dependent compressible Navier-Stokes equations in the low Mach number regime inside a family of domains $(Ω_\varepsilon)_{\varepsilon > 0}$ in $\mathbb{R}^3$. Assuming that $\lim_{\varepsilon \to 0} Ω_\varepsilon = Ω\subset \mathbb{R}^3$ in a suitable sense, we show that in the limit the fluid flow inside $Ω$ is governed by the incompressible Navier-Stokes-Brinkman equations, provided the latter one admits a strong solution. The abstract convergence result is complemented with a stochastic homogenization result for randomly perforated domains in the critical regime.
math.AP↗