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

Abstract

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.

Authors

Fabrice Bethuel

Laboratoire J.-L. Lions, Université Pierre et Marie Curie, 75013 Paris, France and Institut Universitaire de France, 75005 Paris, France

Giandomenico Orlandi

Dipartimento di Informatica, Università di Verona, 37129 Verona, Italy

Didier Smets

Laboratoire J.-L. Lions, Université Pierre et Marie Curie, 75013 Paris, France