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

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

2012-03-20

arxiv.org/abs/1203.4426v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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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