Homogenization of the Navier-Stokes equations in perforated domains in the inviscid limit

We study the solution u(epsilon) to the Navier-Stokes equations in perforated by small particles centered at with no-slip boundary conditions at the particles. We study the behavior of u(epsilon) for small epsilon, depending on the diameter epsilon(alpha), alpha > 1, of the particles and the viscosity epsilon(gamma), gamma > 0, of the fluid. We prove quantitative convergence results for u(epsilon) in all regimes when the local Reynolds number at the particles is negligible. Then, the particles approximately exert a linear friction force on the fluid. The obtained effective macroscopic equations depend on the order of magnitude of the collective friction. We obtain (a) the Euler-Brinkman equations in the critical regime, (b) the Euler equations in the subcritical regime and (c) Darcy's law in the supercritical regime.