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

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
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References:

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