Minimizers of a Landau–de Gennes energy with a subquadratic elastic energy

We study a modified Landau–de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional domains, subject to uniaxial boundary conditions, in the asymptotic regi...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2019-09, Vol.233 (3), p.1169-1210
Main Authors: Canevari, Giacomo, Majumdar, Apala, Stroffolini, Bianca
Format: Article
Language:English
Subjects:
Boundary conditions
Classical Mechanics
Complex Systems
Domains
Fluid- and Aerodynamics
Liquid crystals
Mathematical and Computational Physics
Nematic crystals
Physics
Physics and Astronomy
Singularity (mathematics)
Theoretical
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Summary:We study a modified Landau–de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional domains, subject to uniaxial boundary conditions, in the asymptotic regime where the length scale of the defect cores is small compared to the length scale of the domain. We obtain uniform convergence of the minimizers and of their gradients, away from the singularities of the limiting uniaxial map. We also demonstrate the presence of maximally biaxial cores in minimizers on two-dimensional domains, when the temperature is sufficiently low.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-019-01376-7