Evolution of non-isothermal Landau-de Gennes nematic liquid crystals flows with singular potential

TL;DR

This paper develops a mathematically rigorous 3D model for the evolution of nematic liquid crystals incorporating thermal effects and a singular potential, ensuring physical constraints and global solutions.

Contribution

It introduces a thermodynamically consistent 3D model with a singular potential for nematic liquid crystals and proves the existence of global weak solutions.

Findings

Established a priori estimates for the system

Constructed global-in-time weak solutions

Ensured physical constraints via singular potential

Abstract

We discuss a 3D model describing the time evolution of nematic liquid crystals in the framework of Landau-de Gennes theory, where the natural physical constraints are enforced by a singular free energy bulk potential proposed by J.M. Ball and A. Majumdar. The thermal effects are present through the component of the free energy that accounts for intermolecular interactions. The model is consistent with the general principle of thermodynamics and mathematically tractable. We identify the a priori estimates for the associated system of evolutionary partial differential equations and construct global-in-time weak solutions for arbitrary physically relevant initial data.