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Weak sequential stability for a nonlinear model of nematic electrolytes

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

Weak sequential stability for a nonlinear model of nematic electrolytes

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 velocityfield, and a non-smooth Allen-Cahn type equation for the nematic directorfield. 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.

Keywords

Compactness, A-priori estimates, Navier-Stokes equations for incompressible viscous fluids, Weak-sequential stability, a-priori estimates, weak-sequential stability, Nernst-planck equation, 530, A priori estimates in context of PDEs, 510, Navier-Stokes system, Navier-stokes system, Nernst-Planck equation, compactness, PDEs in connection with optics and electromagnetic theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
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