Ginzburg-Landau Vortices Driven by the Landau-Lifshitz-Gilbert Equation

Matthias Kurzke; Christof Melcher; Roger Moser; Daniel Spirn

doi:10.1007/s00205-010-0356-0

Ginzburg-Landau Vortices Driven by the Landau-Lifshitz-Gilbert Equation

Matthias Kurzke, Christof Melcher, Roger Moser, Daniel Spirn

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular, we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization are ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schrödinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation.

Original language	English (US)
Pages (from-to)	843-888
Number of pages	46
Journal	Archive For Rational Mechanics And Analysis
Volume	199
Issue number	3
DOIs	https://doi.org/10.1007/s00205-010-0356-0
State	Published - Mar 2011

Bibliographical note

Funding Information:
Part of this research was carried out while the authors enjoyed the hospitality of the Hausdorff Research Institute for Mathematics in Bonn. M atthias K urzke was partially supported by DFG SFB 611; D aniel S pirn was partially supported by NSF grant DMS-0707714.

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Ginzburg-Landau Vortices Driven by the Landau-Lifshitz-Gilbert Equation

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