Preprint

Inserted: 15 may 2025
Last Updated: 16 may 2025

Pages: 43
Year: 2025

Abstract:

We consider the time-dependent compressible Navier-Stokes equations in the low Mach number regime inside a family of domains $(\Omega_\varepsilon)_{\varepsilon>0}$ in $\mathbb R^3$. Assuming that $\lim_{\varepsilon\to0}\Omega_\varepsilon=\Omega\subset\mathbb R^3$ in a suitable sense, we show that in the limit the fluid flow inside $\Omega$ 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.

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