Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume 236, Issue 2, Pages 1089-1125Publisher
SPRINGER
DOI: 10.1007/s00205-019-01488-0
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Funding
- Austrian Science Fund (FWF) through the special research program Taming complexity in partial differential systems [SFB F65]
- Vienna Science and Technology Fund (WWTF) through the research project Thermally controlled magnetization dynamics [MA14-44]
- EPSRC [EP/K02390X/1, EP/K032208/1, EP/R014604/1]
- Leverhulme Grant [RPG-2014-226]
- Lady Davis Visiting Professorship at the Hebrew University
- Basque Government through the BERC 2018-2021 program
- Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation [SEV-2017-0718]
- Spanish Ministry of Economy and Competitiveness MINECO - AEI/FEDER, UE [MTM2017-82184-R]
- Isaac Newton Institute for Mathematical Sciences
- EPSRC [EP/K032208/1, EP/R014604/1, EP/K02390X/1] Funding Source: UKRI
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We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, the minimum-energy configurations can be described by the simpler Oseen-Frank theory. Using a refined notion of Gamma-development we recover Landau-de Gennes corrections to the Oseen-Frank energy. We provide an explicit characterisation of minimizing Q-tensors at this order in terms of optimal Oseen-Frank directors and observe the emerging biaxiality. We apply our results to distinguish between optimal configurations in the class of conformal director fields of fixed topological degree saturating the lower bound for the Oseen-Frank energy.
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