Dynamics of multiple degree Ginzburg–Landau vortices |
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Authors: | Fabrice Bethuel Giandomenico Orlandi Didier Smets |
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Institution: | 1. Laboratoire Jacques-Louis Lions, université de Paris 6, 4, place Jussieu, BC 187, 75252 Paris cedex 05, France;2. Institut Universitaire de France;3. Dipartimento di Informatica, Università di Verona, Strada le Grazie, 37134 Verona, Italy |
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Abstract: | For the two-dimensional complex parabolic Ginzburg–Landau equation we prove that, asymptotically, vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the Kirchhoff–Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which we describe carefully. The only assumption is a natural energy bound on the initial data. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). |
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