Open AccessExistence and uniqueness of global classical solutions of a gradient flow of the Landau-de Gennes energy
Author(s) -
Xinfu Chen,
Xiang Xu
Publication year - 2015
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/12803
Subject(s) - algorithm , uniqueness , annotation , type (biology) , computer science , artificial intelligence , mathematics , mathematical analysis , geology , paleontology
In this paper we establish the existence and uniqueness of global classical solutions to a gradient flow in R d \mathbb {R}^d , d ≥ 2 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 Q -tensors. We work in Hölder spaces, and deal with d = 2 d=2 and d ≥ 3 d\geq 3 separately.