Nonlinear electrokinetics in nematic electrolytes

E. Feireisl; E. Rocca; G. Schimperna; A. Zarnescu

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arXiv · 1909.00682

Nonlinear electrokinetics in nematic electrolytes

E. Feireisl·E. Rocca·G. Schimperna·A. Zarnescu

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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.

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BibTeX RIS

E. Feireisl, E. Rocca, G. Schimperna, A. Zarnescu. 2019-09-02. Nonlinear electrokinetics in nematic electrolytes. https://arxiv.org/abs/1909.00682

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