  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.
