Calculus of Variations and Geometric Measure Theory

F. Bethuel - G. Orlandi - D. Smets

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

created on 06 Jun 2003
modified by orlandi on 03 Dec 2005


Published Paper

Inserted: 6 jun 2003
Last Updated: 3 dec 2005

Journal: Ann. of Math.
Volume: 163
Number: 1
Pages: 37-163
Year: 2006


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