Averaging of nonstationary Stokes flow in a periodic porous medium
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 \(\varepsilon\to 0\).
scientific article; zbMATH DE number 1113095