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.
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Acknowledgements
We would like to thank Professor John Ball for his kind discussions, especially pointing out several useful references to us. We thank the anonymous referees for their suggestions to improve the quality of our paper. X. Y. Lu’s work is supported by his NSERC Discovery Grant “Regularity of minimizers and pattern formation in geometric minimization problems.” X. Xu’s work is supported by the NSF Grant DMS-2007157 and the Simons Foundation Grant No. 635288. W. J. Zhang’s work is supported by NSF Grant DMS-1818861.
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Communicated by Eliot Fried.
Dedicated to Professor David Kinderlehrer’s 80th birthday.
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Lu, X.Y., Xu, X. & Zhang, W. Blowup Rate Estimates of a Singular Potential and Its Gradient in the Landau-de Gennes Theory. J Nonlinear Sci 32, 6 (2022). https://doi.org/10.1007/s00332-021-09761-x
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DOI: https://doi.org/10.1007/s00332-021-09761-x