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 ε tends to zero,which is independent of the coordinates towards the thickness.
In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed.
