期刊
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
卷 196, 期 1, 页码 227-280出版社
SPRINGER
DOI: 10.1007/s00205-009-0249-2
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资金
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- EPSRC [EP/E010288/1]
- EPSRC [EP/E010288/1, EP/E035027/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E035027/1, EP/E010288/1] Funding Source: researchfish
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 W (1,2), 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.
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