Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals

Abstract

We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (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.

References in corpus (4)

• Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond
• Orientability and energy minimization in liquid crystal models
• Refined approximation for a class of Landau-de Gennes energy minimizers
• Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals

Cited by in corpus (24)

• Mathematics and liquid crystals
• Half-integer point defects in the $Q$-tensor theory of nematic liquid crystals
• Instability of point defects in a two-dimensional nematic liquid crystal model
• Minimizers of the Landau-de Gennes energy around a spherical colloid particle
• Line defects in the small elastic constant limit of a three-dimensional Landau-de Gennes model
• Spherical particle in a nematic liquid crystal under an external field: the Saturn ring regime
• Torus-like solutions for the Landau-de Gennes model. Part I: the Lyuksyutov regime
• Landau-de Gennes corrections to the Oseen-Frank theory of nematic liquid crystals
• Topological singular set of vector-valued maps, II: $\Gamma$-convergence for Ginzburg-Landau type functionals
• Symmetry and multiplicity of solutions in a two-dimensional Landau-de Gennes model for liquid crystals
• Disclinations in limiting Landau-de Gennes theory
• Singular perturbation of manifold-valued maps with anisotropic energy
• On the Disclination Lines of Nematic Liquid Crystals
• The Radial Hedgehog Solution in the Landau-de Gennes Theory: Effects of the Bulk Potentials
• Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring
• Torus-like solutions for the Landau-de Gennes model. Part II: Topology of ${\mathbb{S}}^1$-equivariant minimizers
• Radial Symmetry on 3D Shells in the Landau-de Gennes Theory
• Pattern Formation in Landau-de Gennes Theory
• Tetrahedral frame fields via constrained third order symmetric tensors
• Liquid crystal defects in the Landau-de Gennes theory in two dimensions-beyond the one-constant approximation
• Stability of half-degree point defect profiles for 2-D nematic liquid crystal
• Stability of point defects of degree $\pm \frac{1}{2}$ in a two-dimensional nematic liquid crystal model
• Stability of axisymmetric chiral skyrmions
• Point defects in 2-D liquid crystals with singular potential: profiles and stability