Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

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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 are ruled by the Landau–Lifshitz–Gilbert equation, which combines characteristic properties of a nonlinear Schrodinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation.