  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.
