INERTIAL EFFECTS FOR A STATIONARY VISCOUS INCOMPRESSIBLE-FLOW IN A POROUS-MEDIUM

We consider the stationary viscous incompressible fluid flow through a rigid porous medium. If the geometric structure of the porous part is periodic with the period epsilon and if the Reynolds number and inver se of Froude's number are of order epsilon(-1) then the formal asympto tic expansion established by E. Sanchez-Palencia and J.-L. Lions gives a homogenized problem called ''Navier-Stokes system with two pressure s'': Supposing that the data are not too large we prove the well-posed ness of the homogenized problem and the convergence of the homogenizat ion process.