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

• Autores: G. Orlandi, Didier Smets, Fabrice Bethuel
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 163, Nº 1, 2006, págs. 37-163
• Idioma: inglés
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• Resumen

  • 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.