Dynamic Cubic Instability in a 2D Q-tensor Model for Liquid Crystals

TL;DR

This paper investigates how a cubic term in a 2D Q-tensor model affects the stability and dynamics of nematic liquid crystals, focusing on the well-posedness and physicality of solutions.

Contribution

It analyzes the impact of a cubic term in the Landau-de Gennes energy on the dynamical behavior and stability of nematic liquid crystal configurations in two dimensions.

Findings

Cubic term can cause instability and unbounded energy from below.

Initial data's physicality influences global well-posedness.

Insights into the dynamical effects of cubic terms in liquid crystal models.

Abstract

We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal configurations described using the $Q$-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical effects produced by the presence of this cubic term by considering an $L^2$ gradient flow generated by this energy. We work in two dimensions and concentrate on understanding the relations between the physicality of the initial data and the global well-posedness of the system.