Qualitative/quantitative homogenization of some non-Newtonian flows in perforated domains

In this paper, we consider the homogenization of stationary and evolutionary incompressible viscous non-Newtonian flows of Carreau-Yasuda type in domains perforated with a large number of periodically distributed small holes in R³, where the mutual distance between the holes is measured by a small parameter ε>0 and the size of the holes is εα with α ∈ (1, 32). The Darcy's law is recovered in the limit, thus generalizing the results from [{https://doi.org/10.1016/0362-546X(94)00285-P}] and [{https://doi.org/10.48550/arXiv.2310.05121}] for α=1. Instead of using their restriction operator to derive the estimates of the pressure extension by duality, we use the Bogovski{} type operator in perforated domains (constructed in [{https://doi.org/10.1051/cocv/2016016}]) to deduce the uniform estimates of the pressure directly. Moreover, quantitative convergence rates are given.