Gamma-convergence of gradient flows with applications to Ginzburg-Landau

Etienne Sandier, Sylvia Serfaty

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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 languageEnglish (US)
Pages (from-to)1627-1672
Number of pages46
JournalCommunications on Pure and Applied Mathematics
Volume57
Issue number12
DOIs
StatePublished - Dec 1 2004

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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