On the existence of skyrmions in planar liquid crystals

DOI10.12775/TMNA.2019.053zbMath1439.82051OpenAlexW2979462781MaRDI QIDQ2178772

Carlo Greco

Publication date: 11 May 2020

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.tmna/1570413618

zbMATH Keywords

skyrmionsconcentration compactnessliquid crystalsBogomol'nyi decomposition

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Statistical mechanics of magnetic materials (82D40) Soliton solutions (35C08) Integro-partial differential equations (35R09)

Related Items (3)

A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree \(\pm 1\) harmonic maps from \(\mathbb{R}^2\) to \(\mathbb{S}^2\) ⋮ Existence criteria for baby skyrmions for a wide range of potentials ⋮ Chiral skyrmions of large radius

Cites Work

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• Existence of 2D Skyrmions
• Large solutions for harmonic maps in two dimensions
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Boundary regularity and the Dirichlet problem for harmonic maps
• A direct variational approach to Skyrme's model for meson fields
• Skyrmion states in chiral liquid crystals
• Compactness results for static and dynamic chiral skyrmions near the conformal limit
• Existence of two-dimensional Skyrmions via the concentration-compactness method
• A non-linear field theory
• The baby Skyrme models and their multi-skyrmions
• Chiral skyrmions in the plane

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