Stability of the Melting Hedgehog in the Landau–de Gennes Theory of Nematic Liquid Crystals

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• 作者：Radu Ignat ; Luc Nguyen ; Valeriy Slastikov…
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：215
• 期：2
• 页码：633-673
• 全文大小：414 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Electromagnetism, Optics and Lasers
  Mathematical and Computational Physics
  Complexity
  Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0673

文摘

We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (the so called “melting hedgehog- in the framework of the Landau–de Gennes model of nematic liquid crystals. We prove local stability of the melting hedgehog under arbitrary Q-tensor valued perturbations in the temperature regime near the critical supercooling temperature. As a consequence of our method, we also rediscover the loss of stability of the vortex defect in the deep nematic regime.