Homogenization of a Uid Problem with a Free Boundary

The stationary Stokes equations with a free boundary are studied in a perforated domain. The perforation consists of a periodic array of cylinders of size and distance O("). The free boundary is given as the graph of a function on a two-dimensional perforated domain. We derive equations for the two-scale limit of solutions. The limiting equation is a free boundary system. It involves a nonlinear elliptic operator corresponding to the nonlinear mean-curvature expression in the original equations. Depending on the equation for the contact-angle the pressure is in general unbounded.