Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations

Christophe Lacave, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size ε separated by distances dε and the fluid fills the exterior. If the inclusions are distributed on the unit square, the asymptotic behavior depends on the limit of dεε when ε goes to zero. If dεε→∞, then the limit motion is not perturbed by the porous medium, namely, we recover the Euler solution in the whole space. If, on the contrary, dεε→0, then the fluid cannot penetrate the porous region, namely, the limit velocity verifies the Euler equations in the exterior of an impermeable square. If the inclusions are distributed on the unit segment then the behavior depends on the geometry of the inclusion: it is determined by the limit of dεε2+1γ where γ∈ (0 , ∞] is related to the geometry of the lateral boundaries of the obstacles. If dεε2+1γ→∞, then the presence of holes is not felt at the limit, whereas an impermeable wall appears if this limit is zero. Therefore, for a distribution in one direction, the critical distance depends on the shape of the inclusions; in particular, it is equal to ε3 for balls.

Original languageEnglish (US)
Pages (from-to)1117-1160
Number of pages44
JournalArchive for Rational Mechanics and Analysis
Volume221
Issue number3
DOIs
StatePublished - Sep 1 2016

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations'. Together they form a unique fingerprint.

Cite this