Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers
arXiv:2109.15178
Abstract
We study the behaviour of global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axially symmetric domains domains diffeomorphic to a ball (a nematic droplet) and in a restricted class of $\bbS^1$-equivariant configurations. It is known from our previous paper \cite{DMP2} that, assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a physically relevant norm constraint in the interior (Lyuksyutov constraint), minimizing configurations are either of \emph{torus} or of \emph{split} type. Here, starting from a nematic droplet with the homeotropic boundary condition, we show how singular (split) solutions or smooth (torus) solutions (or even both) for the Euler-Lagrange equations do appear as energy minimizers by suitably deforming either the domain or the boundary data. As a consequence, when minimizers among $\bbS^1$-equivariant configurations are singular we derive symmetry breaking result for the minimization among all competitors.
arXiv commentPresentation greatly improved. Theorem 1.3 and Theorem 1.4 also improved. Corollary 6.12 added
References in corpus (6)
- Introduction to Q-tensor theory
- Instability of point defects in a two-dimensional nematic liquid crystal model
- Aligned dipolar Bose-Einstein condensate in a double-well potential: From cigar-shaped to pancake-shaped
- Spherical particle in a nematic liquid crystal under an external field: the Saturn ring regime
- The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis
- Symmetry and multiplicity of solutions in a two-dimensional Landau-de Gennes model for liquid crystals