2024/07/29 by Hömberg, Dietmar, Lasarzik, Robert, Plato, Luisa
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2407.19713
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.