Nonlinear electrokinetics in nematic electrolytes
Analysis of PDEs
2019-09-04 v1
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.
Cite
@article{arxiv.1909.00682,
title = {Nonlinear electrokinetics in nematic electrolytes},
author = {E. Feireisl and E. Rocca and G. Schimperna and A. Zarnescu},
journal= {arXiv preprint arXiv:1909.00682},
year = {2019}
}