HOMOGENIZATION OF THE STOKES SYSTEM IN A NON-PERIODICALLY PERFORATED DOMAIN.

In our recent work [X. Blanc and S. Wolf, Asymptot. Anal., 126 (2021), pp. 129-155], we have studied the homogenization of the Poisson equation in a class of non-periodically perforated domains. In this paper, we examine the case of the Stokes system. We consider a porous medium in which the characteristic distance between two holes, denoted by\varepsilon, is proportional to the characteristic size of the holes. It is well known (see [G. Allaire, Asymptot. Anal., 2 (1989), pp. 203-222; E. Sanchez-Palencia, in Non-Homogeneous Media and Vibration Theory, Springer, New York, 1980, pp. 129-157; L. Tartar, in Non-Homogeneous Media and Vibration Theory, Springer, New York, 1980, Appendix]) that, when the holes are periodically distributed in space, the velocity converges to a limit given by Darcy's law when the size of the holes tends to zero. We generalize these results to the setting of [X. Blanc and S. Wolf, Asymptot. Anal., 126 (2021), pp. 129-155]. The nonperiodic domains are defined as a local perturbation of a periodic distribution of holes. We obtain classical results of the homogenization theory in perforated domains (existence of correctors and regularity estimates uniform in\varepsilon) and we prove H²-convergence estimates for particular force fields. [ABSTRACT FROM AUTHOR]