PreprintarXiv licencearXiv
On the minimality of the radial singularity in nematic liquid crystals
Abstract
We show that the map u*: B1⊂ℝ3→𝕊2, x↦ x/|x|, minimizes the anisotropic energy ∫B1 ( k1(div u)2+k2 (u· curl u)2 +k3 |u×curl u|2 ) dx, among 𝕊2-valued maps agreeing with it on the boundary, for values of k1,k2,k3>0 beyond the known regime k1≤ k2. Our main tool is a new stability estimate for u* as a minimizing sphere-valued harmonic map.
Related
- Modeling and Analysis of Cooling Induced Isotropic Nematic Transitions in Pharmaceutical Liquid Crystals
- Global existence of solutions to the 2D compressible nematic liquid crystal flows with large initial data and vacuum
- Global Well-Posedness of Strong Solutions to the Two-Dimensional Compressible Nematic Liquid Crystal Flows with Large Initial Data and Vacuum
- Error estimates for semi-Galerkin approximations of the 3D inhomogeneous nematic liquid crystal flows
- Global Existence and Large-Time Behavior of Strong Solutions to the Two-Dimensional Compressible Nematic Liquid Crystal Flows with Large Initial Data and Vacuum
BibTeX
@misc{bousquet2026minimality,
title = {{On the minimality of the radial singularity in nematic liquid crystals}},
author = {Pierre Bousquet and Xavier Lamy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36972},
eprint = {2609.36972},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36972},
}
RIS
TY - UNPB
TI - On the minimality of the radial singularity in nematic liquid crystals
AU - Pierre Bousquet
AU - Xavier Lamy
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36972
UR - https://arxiv.org/abs/2609.36972
AB - We show that the map u_*: B_1⊂ℝ^3→𝕊^2, x↦ x/|x|, minimizes the anisotropic energy ∫_B_1 ( k_1(div u)^2+k_2 (u· curl u)^2 +k_3 |u×curl u|^2 ) dx, among 𝕊^2-valued maps agreeing with it on the boundary, for values of k_1,k_2,k_3>0 beyond the known regime k_1≤ k_2. Our main tool is a new stability estimate for u_* as a minimizing sphere-valued harmonic map.
ER -