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

Abstract

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.