Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamics-consistency

TL;DR

This paper derives a thermodynamically consistent non-isothermal Ericksen-Leslie model for nematic liquid crystals, analyzing its global well-posedness for small initial data within Besov spaces.

Contribution

It extends the Ericksen-Leslie system to include thermal effects while ensuring thermodynamic consistency and provides a mathematical analysis of the system's well-posedness.

Findings

Model derivation incorporating thermal effects and thermodynamics.

Proof of global-in-time well-posedness for small initial data.

Framework established in Besov spaces for analysis.

Abstract

We derive a model describing the evolution of a nematic liquid-crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen-Leslie system where the Leslie stress tensor and the Oseen-Frank energy density are considered in their general forms. The work postulate proposed by Ericksen-Leslie is traduced in terms of entropy production. We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.