Methods and Applications of Analysis

Volume 22 (2015)

Number 3

The effect of magnetic fields under specific boundary data in the theory of liquid crystals

Pages: 313 – 342

DOI: https://dx.doi.org/10.4310/MAA.2015.v22.n3.a5

Authors

Junichi Aramaki (Division of Science, Faculty of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Saitama, Japan)

Kentaro Chinen (Division of Science, Faculty of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Saitama, Japan)

Yoshiyasu Ito (Division of Science, Faculty of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Saitama, Japan)

Shohei Ono (Division of Science, Faculty of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Saitama, Japan)

Abstract

We consider the response of a magnetic field in the theory of liquid crystals. We treat the Landau–de Gennes functional with the strong anchoring condition which may be non-constant under a magnetic field which may also be non-constant. Such situation is more general than the works of Lin and Pan in 2007 and Aramaki in 2012. We show that there exist two critical points of intensity of the field such that one corresponds to the superheating fields of superconductors and the other one corresponds to stability. We also show that under some special conditions, strong field does not bring the pure nematic state which is very different response from superconductors.

Keywords

effect of magnetic fields, variational problem, liquid crystal

2010 Mathematics Subject Classification

35A15, 35Q60, 47F05, 58E20, 82D30

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Published 1 October 2015