Abstract
We present a method to prove convergence of gradient flows of families of energies that Γ-converge to a limiting energy. It provides lower-bound criteria to obtain the convergence that correspond to a sort of C 1-order Γ-convergence of functionals. We then apply this method to establish the limiting dynamical law of a finite number of vortices for the heat flow of the Ginzburg-Landau energy in dimension 2, retrieving in a different way the existing results for the case without magnetic field and obtaining new results for the case with magnetic field.
Original language | English (US) |
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Pages (from-to) | 1627-1672 |
Number of pages | 46 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 57 |
Issue number | 12 |
DOIs | |
State | Published - Dec 2004 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics