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On the regularity of weak small solution of a gradient flow of the Landau-de Gennes energy


Authors: Tao Huang and Na Zhao
Journal: Proc. Amer. Math. Soc. 147 (2019), 1687-1698
MSC (2010): Primary 53B65, 76A15, 25D30
DOI: https://doi.org/10.1090/proc/14337
Published electronically: January 8, 2019
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Abstract: For a gradient flow of the Landau-de Gennes energy, the unique global weak solution of initial and boundary value problem in dimension two has been constructed by Iyer-Xu-Zarnescu [Math. Models Methods Appl. Sci. 25 (2015), no. 8, 1477-1517] with small initial data. We investigate the regularity of such a solution, and prove that the weak small solution constructed in that paper is actually regular.


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Additional Information

Tao Huang
Affiliation: NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China – and – Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Na Zhao
Affiliation: School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai 200433, China

DOI: https://doi.org/10.1090/proc/14337
Received by editor(s): December 6, 2017
Received by editor(s) in revised form: May 21, 2018, and July 22, 2018
Published electronically: January 8, 2019
Additional Notes: The first author was partially supported by the Natural Science Foundation of Shanghai 16ZR1423800, NSFC 11601333.
The second author served as corresponding author.
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society