LIMITING MOTION FOR THE PARABOLIC GINZBURG-LANDAU EQUATION WITH INFINITE ENERGY DATAReportar como inadecuado




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1 LJLL - Laboratoire Jacques-Louis Lions 2 CMLS - Centre de Mathématiques Laurent Schwartz

Abstract : We study a class of solutions to the parabolic Ginzburg-Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data. We show that, asymptotically, vorticity evolves according to motion by mean curvature in Brakke-s weak formulation. Then, we prove that in the plane, point vortices do not move in the original time scale. These results extend the work of Bethuel, Orlandi and Smets 8, 9 for infinite energy data; they allow to consider the point vortices on a lattice in dimension 2, or filament vortices of infinite length in dimension 3.





Autor: Delphine Côte - Raphaël Côte -

Fuente: https://hal.archives-ouvertes.fr/



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