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Existence and uniqueness of global classical solutions of a gradient flow of the Landau-de Gennes energy


Authors: Xinfu Chen and Xiang Xu
Journal: Proc. Amer. Math. Soc. 144 (2016), 1251-1263
MSC (2010): Primary 35B40, 35B41, 35Q35, 76D05
DOI: https://doi.org/10.1090/proc/12803
Published electronically: July 29, 2015
MathSciNet review: 3447676
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Abstract: In this paper we establish the existence and uniqueness of global classical solutions to a gradient flow in $ \mathbb{R}^d$, $ d\geq 2$. This gradient flow is generated by the Laudau-de Gennes energy functional that involves four elastic-constant terms describing nematic liquid crystal configurations in the space of $ Q$-tensors. We work in Hölder spaces, and deal with $ d=2$ and $ d\geq 3$ separately.


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Additional Information

Xinfu Chen
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: xinfu@pitt.edu

Xiang Xu
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: xu719@purdue.edu

DOI: https://doi.org/10.1090/proc/12803
Received by editor(s): August 4, 2014
Received by editor(s) in revised form: March 20, 2015
Published electronically: July 29, 2015
Communicated by: Catherine Sulem
Article copyright: © Copyright 2015 American Mathematical Society

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