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 εα and we prove that for α small enough (nam...

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Published inAnnales de l'Institut Henri Poincaré. Analyse non linéaire Vol. 32; no. 1; pp. 159 - 182
Main Authors Bonnaillie-Noël, V., Lacave, C., Masmoudi, N.
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.01.2015
EMS
Subjects
Analysis of PDEs
Mathematical Physics
Mathematics
Physics
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Summary: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 εα 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→0.
ISSN:0294-1449
1873-1430
DOI:10.1016/j.anihpc.2013.11.002