Homogénéisation des équations de Stokes et de Navier-Stokes dans des domaines perforés périodiquement avec des conditions aux limites de type Fourier. (Homogenization of Stokes and Navier-Stokes equations in periodically perforated domains with boundary conditions of Fourier type). (French) Zbl 0566.35079

The author outlines mathematically the macroscopic behaviour of the motion of an incompressible viscous Newtonian fluid in a periodically perforated domain when the boundary conditions are of Fourier or Neumann’s type on the boundary of the holes. The main result of the paper shows that in some cases the average or macroscopic flow is represented by the motion of a compressible fluid. This note is written in such a way that only a precise formulation of the theorems is presented, and the proofs of them can be found in the paper reviewed below.


35Q30 Navier-Stokes equations
35C20 Asymptotic expansions of solutions to PDEs


Zbl 0566.35080