Darcy’s law as low Mach and homogenization limit of a compressible fluid in perforated domains

We consider the homogenization limit of compressible barotropic Navier–Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. study regime particle sizes and distances such that volume fraction particles tends to zero but their resistance density infinity. Assuming Mach number is decreasing with certain rate, rescaled velocity pressure microscopic system converges solution an effective equation which given Darcy’s law. The range we exactly same leads law incompressible fluids. Unlike previous results for Darcy estimate deficit related approximation via Bogovskiĭ operator. This allows more flexible estimates Lebesgue Sobolev spaces proof convergence all exponents [Formula: see text].