Singularities of divergence-free vector fields with values into \(S^1\) or \(S^2\): applications to micromagnetics
type: Item
instance of: scholarly article
title: Singularities of divergence-free vector fields with values into \(S^1\) or \(S^2\): applications to micromagnetics
zbMATH Open document ID: 1262.35194
DOI: 10.1142/S1793744212300012
author: Radu Ignat
published in: Confluentes Mathematici
publication date: 2013-01-30T00:00:00Z
review text: This survey paper deals with the structure of 2D and 3D unit-length vector fields of vanishing divergence and applications to micromagnetics. In the first part, the author analyzes the regularizing effect, rigidity and approximation results of 2D unit-length divergence-free vector fields. The first aim is to characterize the structure of singularities such as point-singularities (vortices) under the hypothesis of Sobolev regularity of these vector fields. A second issue concerns the study of line-energies concentrated on singularities of codimension 1 of \(S^1\)-valued BV vector fields of vanishing divergence. The second part of this paper focuses on micromagnetics, more precisely, on the analysis of pattern formation of the magnetization. In particular, the author describes domain walls in the thin ferromagnetic films (symmetric Néel walls, asymmetric Néel walls, asymmetric Bloch walls) together with interior and boundary vortices.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35Q82
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 49L25
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 58E50
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 74G65
Mathematics Subject Classification ID: 82D40
zbMATH DE Number: 6132703
zbMATH Keywords: eikonal equation
zbMATH Keywords: regularity
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: kinetic formulation
zbMATH Keywords: {\(\Gamma\)}-convergence
zbMATH Keywords: domain walls
zbMATH Keywords: Ginzburg-Landau theory
zbMATH Keywords: interior and boundary vortices
MaRDI profile type: Publication
full work available at URL: s1793744212300012
OpenAlex ID: W2056402155
description: scientific article; zbMATH DE number 6132703