Abstract
An incompressible fluid is assumed to satisfy the time-independent Stokes equations in a porous medium. The porous medium is modeled by a bounded domain inRnthat is perforated for eachε>0 byε-dilations of a subset ofRnarising from a family of stochastic processes which generalize the homogeneous random fields. The solution of the Stokes equations on these perforated domains is homogenized asε→0 by means of stochastic two-scale convergence in the mean and the homogenized limit is shown to satisfy a two-pressure Stokes system containing both deterministic and stochastic derivatives and a Darcy-type law which generalizes the Darcy law obtained for fluid flow in periodically perforated porous media.
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