Existence and uniqueness of global classical solutions of a gradient flow of the Landau-de Gennes energy
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- by Xinfu Chen and Xiang Xu PDF
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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.References
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Additional Information
- Xinfu Chen
- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- MR Author ID: 261335
- Email: xinfu@pitt.edu
- Xiang Xu
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 817191
- Email: xu719@purdue.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1251-1263
- MSC (2010): Primary 35B40, 35B41, 35Q35, 76D05
- DOI: https://doi.org/10.1090/proc/12803
- MathSciNet review: 3447676