Homogenization of a stationary navier-stokes flow in porous medium with thin film

The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition. At the end of the article, “Darcy's law” is rigorously derived from this model as the parameter ɛ tends to zero, which is independent of the coordinates towards the thickness.