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- W3204299631 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." @default.
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- W3204299631 date "2021-09-30" @default.
- W3204299631 modified "2023-09-27" @default.
- W3204299631 title "Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers" @default.
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