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Volume 25, Issue 3
The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals

Junichi Aramaki

DOI: 10.4208/jpde.v25.n3.5

J. Part. Diff. Eq., 25 (2012), pp. 276-294.

Published online: 2012-09

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  • Abstract

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.

  • Keywords

Freedricksz transition variational problem liquid crystals Landau-de Gennes functional

  • AMS Subject Headings

82D30, 35A15, 58E50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

aramaki@mail.dendai.ac.jp (Junichi Aramaki)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-276, author = {Aramaki , Junichi}, title = {The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {3}, pages = {276--294}, abstract = {

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/5187.html} }
TY - JOUR T1 - The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals AU - Aramaki , Junichi JO - Journal of Partial Differential Equations VL - 3 SP - 276 EP - 294 PY - 2012 DA - 2012/09 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n3.5 UR - https://global-sci.org/intro/article_detail/jpde/5187.html KW - Freedricksz transition KW - variational problem KW - liquid crystals KW - Landau-de Gennes functional AB -

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.

Aramaki , Junichi. (2012). The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals. Journal of Partial Differential Equations. 25 (3). 276-294. doi:10.4208/jpde.v25.n3.5
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