  The steady motion of a viscous incompressible fluid in a multiply-connected,
planar, bounded domain (perforated with a large number of small holes) is
modeled through the Navier-Stokes equations with non-homogeneous Dirichlet
boundary data satisfying the general outflow condition. Under either a symmetry
assumption on the data or under a smallness condition on each of the boundary
fluxes (therefore, no constraints on the magnitude of the boundary velocity are
imposed), we apply the classical energy method in homogenization theory and
study the asymptotic behavior of the solutions to this system as the size of
the perforations goes to zero: it is shown that the effective equations remain
unmodified in the limit. The main novelty of the present work lies in the
obtainment of the required uniform bounds, which are achieved by a
contradiction argument based on Bernoulli's law for solutions of the stationary
Euler equations.
