Permeability through a perforated domain for the incompressible 2D Euler equations

We investigate the influence of a perforated domain on the 2D Euler equations. Small inclusions of size ε   are uniformly distributed on the unit segment or a rectangle, and the fluid fills the exterior. These inclusions are at least separated by a distance εαεα and we prove that for α   small enough (namely, less than 2 in the case of the segment, and less than 1 in the case of the square), the limit behavior of the ideal fluid does not feel the effect of the perforated domain at leading order when ε→0ε→0.