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)|
|Number of pages||25|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Mar 2014|
Bibliographical noteFunding Information:
M. Kurzke was supported by DFG SFB 611. D. Spirn was partially supported by NSF grant DMS-0955687.