Homogenization of the inviscid incompressible fluid flow through a 2D porous medium

We consider the non-stationary incompressible Euler equations in a 2D porou s medium. We suppose a periodic porous medium, with the period proportional to the characteristic pore size epsilon and with connected fluid part. The ow is subject to an external force, corresponding to an in ow. We start fr om an initial irrotational velocity and prove that the effective filtration velocity satisfies a transient filtration law. It has similarities with Da rcy's law, but it now connects the time derivative of the filtration veloci ty with the pressure gradient. The viscosity does not appear in the filtrat ion law any more and the permeability tensor is determined through auxiliar y problems of decomposition type. Using the limit problem, we construct the correction for the fluid velocity and prove that C-1([0, T]; L-2(Ohm)(2))- norm of the error is of order epsilon. Similarly, we estimate the differenc e between the fluid pressure and its correction in C([0, T]; L-1(Ohm)) as C epsilon.