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Averaging of nonstationary Stokes flow in a periodic porous medium. (English. Russian original) Zbl 0890.35106
Dokl. Math. 53, No. 2, 211-214 (1996); translation from Dokl. Akad. Nauk 347, No. 3, 312-315 (1996).
A nonstationary system of Stokes equations in a periodically perforated domain with a small period \(\varepsilon\) is considered. The system simulates the flow of a viscous incompressible liquid in a periodic porous medium at the level of a linear approximation. It is assumed that the viscosity coefficient \(v\) in the system satisfies one of the following three conditions when \(\varepsilon\to 0\): \[ v/\varepsilon^2\to \infty,\quad v/\varepsilon^2\to 1,\quad v/\varepsilon^2\to 0. \] Averaged equations, whose forms depend on the limiting behavior of the viscosity coefficient, are presented. We also consider some extensions to solutions of the system and formulate statements on their convergence to solutions of the averaged equations when \(\varepsilon\to 0\).
35Q30 Navier-Stokes equations
76S05 Flows in porous media; filtration; seepage
76D07 Stokes and related (Oseen, etc.) flows