A new approach to non-isothermal models for nematic liquid crystals

TL;DR

This paper presents a novel class of non-isothermal models for nematic liquid crystals that align with thermodynamic principles and include director field stretching effects, ensuring global weak solutions without initial data restrictions.

Contribution

It introduces a new thermodynamically consistent modeling framework for nematic liquid crystals that accounts for director stretching and guarantees global solutions.

Findings

Models are consistent with classical thermodynamics

Existence of global-in-time weak solutions

Inclusion of director field stretching effects

Abstract

We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical Thermodynamics. The resulting system of equations captures all essential features of physically relevant models, in particular, the effect of stretching of the director field is taken into account. In addition, the associated initial-boundary value problem admits global-in-time weak solutions without any essential restrictions on the size of the initial data.