Corrector homogenization estimates for a non-stationary Stokes-Nernst-Planck-Poisson system in perforated domains

We consider a non-stationary Stokes-Nernst-Planck-Poisson system posed in perforated domains. Our aim is to justify rigorously the homogenization limit for the upscaled system derived by means of two-scale convergence in \cite{RMK12}. In other words, we wish to obtain the so-called corrector homogenization estimates that specify the error obtained when upscaling the microscopic equations. Essentially, we control in terms of suitable norms differences between the micro- and macro-concentrations and between the corresponding micro- and macro-concentration gradients. The major challenges that we face are the coupled flux structure of the system, the nonlinear drift terms and the presence of the microstructures. Employing various energy-like estimates, we discuss several scalings choices and boundary conditions.
Comment: 34 pages, 2 figures, 1 table