Ginzburg-Landau vortices driven by the Landau-Lifshitz equation

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schrödinger equation and a gradient flow. We study the motion of the vortex centres under this evolution equation.

This is a joint work with Matthias Kurzke (University of Bonn), Christof Melcher (RWTH Aachen), and Daniel Spirn (University of Minnesota).