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Homogenization of non-stationary Stokes equations with viscosity in a perforated domain. (English. Russian original) Zbl 0893.35095
Izv. Math. 61, No. 1, 113-141 (1997); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 61, No. 1, 113-140 (1997).
The author considers an initial boundary-value problem for non-stationary Stokes equations in a periodic perforated domain with a small period \(\varepsilon\). These equations simulate the linearized incompressible viscous fluid flow through a periodic porous medium. He assumes that the viscosity coefficient \(\nu\) of these equations satisfies one of the following conditions as \(\varepsilon\rightarrow 0\): \(\nu/\varepsilon^{2}\rightarrow\infty\), \(\nu/\varepsilon^{2}\rightarrow 1\), \(\nu/\varepsilon^{2}\rightarrow 0\). Then he derives the homogenized (averaged) equations, whose form depends on the asymptotic behaviour of the viscous coefficient, and proves that the solutions of the Stokes equations converge (in appropriate spaces) to the solutions of the homogenized equations as \(\varepsilon\rightarrow 0\).
Reviewer: F.Rosso (Firenze)

35Q30 Navier-Stokes equations
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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