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Homogenization of the Navier‐Stokes equations with a slip boundary condition
Author(s) -
Allaire Grégoires
Publication year - 1991
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160440602
Subject(s) - homogenization (climate) , mathematics , dirichlet boundary condition , mathematical analysis , boundary value problem , stokes flow , navier–stokes equations , slip (aerodynamics) , geometry , mechanics , physics , biodiversity , ecology , flow (mathematics) , compressibility , biology , thermodynamics
This paper deals with the homogenization of the Stokes or Navier‐Stokes equations in a domain containing periodically distributed obstacles, with a slip boundary condition (i.e., the normal component of the velocity is equal to zero, while the tangential velocity is proportional to the tangential component of the normal stress). We generalize our previous results (see [1]) established in the case of a Dirichlet boundary condition; in particular, for a so‐called critical size of the obstacles (equal to ε 3 in the three‐dimensional case, ε being the inter‐hole distance), we prove the convergence of the homogenization process to a Brinkman‐type law.