Homogenization of the Navier‐Stokes equations with a slip boundary condition

Source abstract

Abstract 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.