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 $\varepsilon$ 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 $\varepsilon^α$ 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 $\varepsilon\to 0$.

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