Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond

Apala Majumdar, Arghir Zarnescu

Research output: Contribution to journalArticlepeer-review

162 Scopus citations


We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W1,2, to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions. © Springer-Verlag (2009).
Original languageEnglish (US)
Pages (from-to)227-280
Number of pages54
JournalArchive for Rational Mechanics and Analysis
Issue number1
StatePublished - Jul 7 2009
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: A. Majumdar was supported by a Royal Commission for the Exhibition of 1851 Research Fellowship till October 2008. She is now supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST), to the Oxford Centre for Collaborative Applied Mathematics. A. Zarnescu is supported by the EPSRC Grant EP/E010288/1-Equilibrium Liquid Crystal Configurations: Energetics, Singularities and Applications. We thank John M. Ball and Christ of Melcher for stimulating discussions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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