Blowup Rate Estimates of a Singular Potential and Its Gradient in the Landau-de Gennes Theory

Xin Yang Lu, Xiang Xu, Wujun Zhang

Research output: Contribution to journalArticlepeer-review

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 Maier–Saupe type singular potential was originally introduced in Katriel et al. (Mol Cryst Liquid Cryst 1:337–355, 1986), which 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. All of the proofs are elementary.

Original languageEnglish (US)
Article number6
JournalJournal of Nonlinear Science
Volume32
Issue number1
DOIs
StatePublished - Feb 2022

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

Keywords

  • 35B44
  • 35Q82
  • Blowup rate
  • Liquid crystals
  • Q-tensor
  • Singular potential

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