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

Matthias Kurzke, Christof Melcher, Roger Moser, Daniel Spirn

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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 languageEnglish
Pages (from-to)1019-1043
JournalCalculus of Variations and Partial Differential Equations
Issue number3-4
Publication statusPublished - Mar 2014


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