Nonlinear theory of defects in nematic liquid crystals; phase transition and flow phenomena. (English) Zbl 0703.35173
The author deals mainly with the question of defect lines in nematic crystals, i.e. lines along which the optical director n is singular. After a long (but necessary) introductory section he discusses how to modify the energy functional in the Oseen-Frank model in order to cope with the difficulty arising from its possible divergence. The basic idea is to introduce a divergence-free field Q, playing the role of the order parameter of Landau’s theory: \(Q=s(n\otimes n-I/3)\), \(| n| =1\), s being a space-dependent scalar, called the degree of orientation. Q replaces n in the energy integral. Under some simplifying assumptions the problem is reduced to finding a minimizing pair (s,u), \(u=sn\). Existence and Hölder continuity of the solutions are also discussed. The final section is devoted to dynamic models.
Reviewer: A.Fasano
MSC:
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
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