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

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.


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