Weak sequential stability for a nonlinear model of nematic electrolytes

Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Zarnescu, Arghir

doi:10.3934/dcdss.2020366

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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Titolo:	Weak sequential stability for a nonlinear model of nematic electrolytes
Autori:	Feireisl, Eduard ROCCA, ELISABETTA (Corresponding) SCHIMPERNA, GIULIO FERNANDO Zarnescu, Arghir mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	Being printed
Rivista:	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S
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.
Handle:	http://hdl.handle.net/11571/1364694
Appare nelle tipologie:	1.1 Articolo in rivista

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