Homogenization of the Stokes Equations with General Random Coefficients

When an attempt is made to model fluid flow in a porous medium, one is often lead to the homogenization problem for the Stokes system. One considers for each value of a small positive parameter e the solution (ui, p ) of a Stokes system with coefficients and boundary conditions depending randomly on E, and one seeks to prove that (u i , p) converges in some sense as C 0 to a limit, and to derive equations which this homogenized limit satisfies. In this paper, we concentrate on the special but interesting case of c-independent Dirichlet boundary conditions and general random coefficients for n-dimensional Stokes systems, and we use the method of stochastic two-scale convergence in the mean, introduced and studied in [3], to solve in a fairly direct and elegant way both of these problems.