On the application of the homogenization theory to a class of problems arising in fluid mechanics. (English) Zbl 0566.35080

Conca, Carlos

J. Math. Pures Appl., IX. Sér. 64, 31-75 (1985).

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)].

MSC:

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

Keywords:

asymptotic expansions; incompressible viscous fluid flows; periodically perforated domain; homogenization theory; macroscopic and microscopic behaviour; numerical computation

Citations:

Zbl 0566.35079