Existence of weak solutions to an anisotropic electrokinetic flow model

Abstract

In this article we present a system of coupled non-linear PDEs modelling 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 modelled by a Navier--Stokes--Nernst--Planck--Poisson system and the anisotropy is introduced via space dependent diffusion matrices in the Nernst--Planck and Poisson equation.