Smooth Convergence of Landau-de Gennes Minimizers in the Lyuksyutov Regime

Abstract

In this paper, we analyze global minimizers of the Landau--de Gennes functional in 3-dimensional domains in the Lyuksyutov regime. We prove smooth convergence to an $\mathbb{S}^4$-valued limit and obtain an $O(μ^{-1})$ estimate for the distance to $\mathbb{S}^4$ as $μ\to +\infty$, thereby extending the convergence results of Dipasquale et al.[Arch. Ration. Mech. Anal. 239: 599--678, 2021].