Nonlinear law for flow between two wavy plates. (Loi d’écoulement non linéaire entre deux plaques ondulées.) (French. Abridged English version) Zbl 0841.76082

Bourgeat, Alain; Marušić-Paloka, Eduard

C. R. Acad. Sci., Paris, Sér. I 321, No. 8, 1115-1120 (1995).

Summary: We consider the stationary viscous incompressible flow through a periodically constricted channel with period and thickness \(\varepsilon\), governed by a strong injection of order \(\varepsilon^{-1}\). We prove the well-posedness of the homogenized problem and the convergence of the homogenization process. A nonlinear filtration law is obtained, and Taylor’s expansion of the filtration velocity is given as a function of the pressure gradient.

MSC:

76S05	Flows in porous media; filtration; seepage
76D05	Navier-Stokes equations for incompressible viscous fluids
35B27	Homogenization in context of PDEs; PDEs in media with periodic structure

Keywords:

two-scale homogenized problem; pressure gradient; periodically constricted channel; strong injection; well-posedness; convergence; Taylor’s expansion; filtration velocity