Singularities of divergence-free vector fields with values into \(S^1\) or \(S^2\): applications to micromagnetics
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.
scientific article; zbMATH DE number 6132703