Homogenization of the evolutionary Navier-Stokes system (Q2634743)

The unsteady flow of an incompressible Navier-Stokes fluid in a perforated bounded domain in \(\mathbb R^3\) is studied, when the number of obstacles tends to infinity. The distance between obstacles is of order \(\epsilon\). A new term of Brinkman's type appears in the limit problem, when the obstacles diameters do no exceed the value \(\epsilon^3\). The Tartar's restriction operator is obtained under mild hypothesis concerning the spatial distribution of obstacles, compared with previous results in homogenization theory. However, the condition \(G\) -- page 225 -- is imposed on the obstacles boundaries, related with the closed cone property. An important tool is the method given in [\textit{G. Acosta} et al., Adv. Math. 206, No. 2, 373--401 (2006; Zbl 1142.35008)]. The Bogovskii operator, related with the inverse of the divergence operator in the perforated domain is also used.