Homogenization of non-stationary Stokes equations with viscosity in a perforated domain

Theorems are proved about the asymptotic behaviour of solutions of an initial boundary-value problem for non-stationary Stokes equations in a periodic perforated domain with a small period $\varepsilon$. The viscosity coefficient $\nu$ of the equations is assumed to be a positive parameter satisfying one of the following three conditions: $\nu/\varepsilon^2 \to \infty,1,0$ as $\varepsilon\to 0$. We also consider the case of degenerate Stokes equations with zero viscosity coefficient and the case of Navier–Stokes equations when the viscosity coefficient is not too small.