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Nonlinear effects for flow in periodically constricted channel caused by high injection rate. (English) Zbl 0920.76082

Summary: We consider a stationary viscous incompressible flow through a periodically constricted channel with the 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. We obtain a nonlinear filtration law and we give the Taylor expansion of the filtration velocity 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
35Q30 Navier-Stokes equations
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