Permeability through a perforated domain for the incompressible 2D Euler equations
V. Bonnaillie-Noël
IRMAR - UMR6625, ENS Rennes, Univ. Rennes 1, CNRS, UEB, av Robert Schuman, 35170 Bruz, FranceC. Lacave
Université Paris-Diderot (Paris 7), Institut de Mathématiques de Jussieu - Paris Rive Gauche, UMR 7586 - CNRS, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, FranceN. Masmoudi
Courant Institute, 251 Mercer St., New York, NY 10012, USA
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Abstract
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 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 .
Cite this article
V. Bonnaillie-Noël, C. Lacave, N. Masmoudi, Permeability through a perforated domain for the incompressible 2D Euler equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, pp. 159–182
DOI 10.1016/J.ANIHPC.2013.11.002