Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature
Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature
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.