Refined Asymptotics for Landau-de Gennes Minimizers on Planar Domains

TL;DR

This paper refines the understanding of minimizers of the Landau-de Gennes energy in planar domains, providing sharper asymptotic descriptions and explicit energy expressions for small correlation lengths.

Contribution

It improves previous asymptotic results by sharpening the description of the limiting map and deriving an explicit energy expression for small but fixed correlation lengths.

Findings

Sharpened asymptotic description of minimizers

Explicit energy formula for small correlation lengths

Enhanced understanding of Landau-de Gennes minimizers

Abstract

In our previous work,, we studied asymptotic behavior of minimizers of the Landau-de Gennes energy functional on planar domains as the nematic correlation length converges to zero. Here we improve upon those results, in particular by sharpening the description of the limiting map of the minimizers. We also provide an expression for the energy valid for a small, but fixed value of the nematic correlation length.