Blowup rate estimates of the Ball-Majumdar potential and its gradient in the Landau-de Gennes theory

TL;DR

This paper analyzes the blowup behavior of the Ball-Majumdar potential and its gradient in the Landau-de Gennes theory, providing insights into the singularities as the Q-tensor approaches physical boundaries.

Contribution

It establishes the blowup rates of the Ball-Majumdar potential and its gradient near the physical boundary of the Q-tensor in nematic liquid crystal models.

Findings

Blowup rates of the potential are characterized as Q approaches boundary.

Blowup rates of the gradient of the potential are determined.

Results enhance understanding of singularities in liquid crystal models.

Abstract

In this paper we revisit a singular bulk potential in the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the framework of the Q-tensor order parameter. This singular potential, called Ball-Majumdar potential, is introduced in [3], and is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. Specifically, we establish blowup rates of both this singular potential and its gradient as Q approaches its physical boundary.