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

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Abstract

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.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, bât. 1R3, 118 Route de Narbonne, 31062, Toulouse, France

    Radu Ignat

  2. Mathematical Insitute and St Edmund Hall, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK

    Luc Nguyen

  3. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    Valeriy Slastikov

  4. Department of Mathematics, University of Sussex, Pevensey 2, Falmer, BN1 9QH, UK

    Arghir Zarnescu

Authors
  1. Radu Ignat
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  2. Luc Nguyen
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  3. Valeriy Slastikov
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  4. Arghir Zarnescu
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Corresponding author

Correspondence to Valeriy Slastikov.

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Communicated by F. Lin

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Ignat, R., Nguyen, L., Slastikov, V. et al. Stability of the Melting Hedgehog in the Landau–de Gennes Theory of Nematic Liquid Crystals. Arch Rational Mech Anal 215, 633–673 (2015). https://doi.org/10.1007/s00205-014-0791-4

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  • DOI: https://doi.org/10.1007/s00205-014-0791-4

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