期刊
JOURNAL OF NONLINEAR SCIENCE
卷 26, 期 1, 页码 121-140出版社
SPRINGER
DOI: 10.1007/s00332-015-9271-8
关键词
Nonlinear elliptic PDE system; Singular ODE system; Stability; Vortex; Liquid crystal defects
资金
- EPSRC [EP/K02390X/1, EP/I028714/1]
- EPSRC [EP/I028714/1, EP/K02390X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K02390X/1, EP/I028714/1] Funding Source: researchfish
We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau-de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, small, we prove that this critical point is the unique global minimiser of the Landau-de Gennes energy. For the case , we investigate in greater detail the regime of vanishing elastic constant , where we obtain three explicit point defect profiles, including the global minimiser.
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