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.

中文翻译：

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向列电解质非线性模型的弱序稳定性

在本文中，我们研究了一种非线性PDE系统，该系统模拟了向列型电解质材料的电动力学，该材料由向列型液晶中包含的各种离子组成。该过程通过将能斯特离子浓度的Nernst-Planck系统与麦克斯韦方程耦合的系统来描述。控制静电势发展的静电方程，用于速度场的Navier-Stokes方程和用于向列方向性场的非光滑Allen-Cahn型方程。我们着眼于两种情况，并证明先验估计提供弱的顺序稳定性结果，这是证明弱解存在的主要步骤。