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

Virginie Bonnaillie-Noël, Christophe Lacave, Nader Masmoudi

Published 2013-06-17Version 1

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 $\varepsilon^\alpha$ and we prove that for $\alpha$ 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 $\varepsilon\to 0$.