Existence of suitable weak solutions to an anisotropic electrokinetic flow model

In this article we present a system of coupled non-linear PDEs modeling an anisotropic electrokinetic flow. We show the existence of suitable weak solutions in three spatial dimensions, that is weak solutions which fulfill an energy inequality, via a regularized system. The flow is modeled by a Navier–Stokes–Nernst–Planck–Poisson system and the anisotropy is introduced via space dependent diffusion matrices in the Nernst–Planck and Poisson equations.