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On the application of the homogenization theory to a class of problems arising in fluid mechanics. (English) Zbl 0566.35080
We study in this paper asymptotic expansions and some theoretical results of convergence for an extensive class of incompressible viscous fluid flows verifying nonstandard boundary conditions on the boundary of a periodically perforated domain. This study uses the homogenization theory on an essentially way; it leads to new properties of the macroscopic and microscopic behaviour of the solutions of Stokes and Navier-Stokes equations. The effective numerical computation of the approximate (or homogenized) solution and of the first corrector terms will be discussed in a forthcoming paper [Proc. Large Scale Computation in Fluid Mechanics (S. Osher (ed.)) (1985)].

35Q30 Navier-Stokes equations
35C20 Asymptotic expansions of solutions to PDEs
Zbl 0566.35079