Inserted: 6 jun 2003
Last Updated: 3 dec 2005
Journal: Ann. of Math.
For the complex parabolic Ginzburg-Landau equation, we prove that, asymptotically, vorticity evolves according to motion by mean curvature in Brakke's weak formulation. The only assumption is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen.
Keywords: parabolic equations, mean curvature flow, Ginzburg-Landau