Nonlinear electrokinetics in nematic electrolytes

TL;DR

This paper models the complex electrokinetic behavior of nematic electrolytes using coupled nonlinear PDEs, establishing foundational stability results for future solution existence proofs.

Contribution

It introduces a comprehensive mathematical model coupling ion transport, electrostatics, fluid flow, and nematic director dynamics, with new stability analysis for weak solutions.

Findings

Established a priori estimates for the coupled PDE system.

Proved weak sequential stability of solutions.

Paved the way for proving existence of weak solutions.

Abstract

In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a system coupling a Nernst-Planck system for the ions concentrations with a Maxwell's equation of electrostatics governing the evolution of the electrostatic potential, a Navier-Stokes equation for the velocity field, and a non-smooth Allen-Cahn type equation for the nematic director field. We focus on the two-species case and prove apriori estimates that provide a weak sequential stability result, the main step towards proving the existence of weak solutions.