Homogenization of nonstationary Navier-Stokes equations in a domain with a grained boundary. (English) Zbl 0758.35007

Mikelić, A.

Ann. Mat. Pura Appl., IV. Ser. 158, 167-179 (1991).

Summary: We prove the convergence of the homogenization process for a nonstationary Navier-Stokes system in a porous medium. The result of homogenization is Darcy’s law, as in the case of the Stokes equation, but the convergence of pressures is in a different function space.

MSC:

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

Keywords:

a priori estimates for pressure; convergence of the homogenization process; Darcy’s law

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