Existence of suitable weak solutions to an anisotropic electrokinetic flow model

TL;DR

This paper proves the existence of suitable weak solutions for a complex anisotropic electrokinetic flow model described by coupled nonlinear PDEs, using a regularized system approach in three dimensions.

Contribution

It establishes the existence of suitable weak solutions for an anisotropic Navier–Stokes–Nernst–Planck–Poisson system, incorporating space-dependent diffusion matrices.

Findings

Existence of suitable weak solutions proven in three dimensions.

Handling of anisotropy through space-dependent diffusion matrices.

Use of regularized system to establish energy inequalities.

Abstract

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.