Geodesic
Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature
Fabrice Bethuel1 ; Giandomenico Orlandi2 ; Didier Smets3
1 Laboratoire J.-L. Lions, Université Pierre et Marie Curie, 75013 Paris, France and Institut Universitaire de France, 75005 Paris, France
2 Dipartimento di Informatica, Università di Verona, 37129 Verona, Italy
3 Laboratoire J.-L. Lions, Université Pierre et Marie Curie, 75013 Paris, France
Annals of mathematics, Tome 163 (2006) no. 1, pp. 37-163.

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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.
DOI : 10.4007/annals.2006.163.37

Fabrice Bethuel 1 ; Giandomenico Orlandi 2 ; Didier Smets 3

1 Laboratoire J.-L. Lions, Université Pierre et Marie Curie, 75013 Paris, France and Institut Universitaire de France, 75005 Paris, France
2 Dipartimento di Informatica, Università di Verona, 37129 Verona, Italy
3 Laboratoire J.-L. Lions, Université Pierre et Marie Curie, 75013 Paris, France 
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Fabrice Bethuel; Giandomenico Orlandi; Didier Smets. Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature. Annals of mathematics, Tome 163 (2006) no. 1, pp. 37-163. doi : 10.4007/annals.2006.163.37. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.37/

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