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 $\mathbb {R}^d$, $d\geq 2$. 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.