Vortex dynamics in the presence of excess energy for the Landau-Lifshitz-Gilbert equation

Matthias Kurzke; Christof Melcher; Roger Moser; Daniel Spirn

doi:10.1007/s00526-013-0609-5

Vortex dynamics in the presence of excess energy for the Landau-Lifshitz-Gilbert equation

Matthias Kurzke, Christof Melcher, Roger Moser, Daniel Spirn

Mathematics

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2 Scopus citations

Abstract

We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We present a PDE-based method for proving vortex dynamics that does not rely on strong well-preparedness of the initial data and allows for instantaneous changes in the strength of the gyrovector force due to bubbling events. The main tools are estimates of the Hodge decomposition of the supercurrent and an analysis of the defect measure of weak convergence of the stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the presence of excess energy are also discussed.

Original language	English (US)
Pages (from-to)	1019-1043
Number of pages	25
Journal	Calculus of Variations and Partial Differential Equations
Volume	49
Issue number	3-4
DOIs	https://doi.org/10.1007/s00526-013-0609-5
State	Published - Mar 2014

Bibliographical note

Funding Information:
M. Kurzke was supported by DFG SFB 611. D. Spirn was partially supported by NSF grant DMS-0955687.

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abstract = "We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We present a PDE-based method for proving vortex dynamics that does not rely on strong well-preparedness of the initial data and allows for instantaneous changes in the strength of the gyrovector force due to bubbling events. The main tools are estimates of the Hodge decomposition of the supercurrent and an analysis of the defect measure of weak convergence of the stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the presence of excess energy are also discussed.",

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AU - Moser, Roger

AU - Spirn, Daniel

N1 - Funding Information: M. Kurzke was supported by DFG SFB 611. D. Spirn was partially supported by NSF grant DMS-0955687.

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AB - We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We present a PDE-based method for proving vortex dynamics that does not rely on strong well-preparedness of the initial data and allows for instantaneous changes in the strength of the gyrovector force due to bubbling events. The main tools are estimates of the Hodge decomposition of the supercurrent and an analysis of the defect measure of weak convergence of the stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the presence of excess energy are also discussed.

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Vortex dynamics in the presence of excess energy for the Landau-Lifshitz-Gilbert equation

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