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

Etienne Sandier, Sylvia Serfaty

Research output: Contribution to journalArticle

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 2004

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Gamma Convergence
Gradient Flow
Ginzburg-Landau
Magnetic fields
Limiting
Energy
Magnetic Field
Vortex flow
Heat Flow
Order of Convergence
Heat transfer
Sort
Vortex
Lower bound
Converge

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Gamma-convergence of gradient flows with applications to Ginzburg-Landau. / Sandier, Etienne; Serfaty, Sylvia.

In: Communications on Pure and Applied Mathematics, Vol. 57, No. 12, 12.2004, p. 1627-1672.

Research output: Contribution to journalArticle

Sandier, Etienne ; Serfaty, Sylvia. / Gamma-convergence of gradient flows with applications to Ginzburg-Landau. In: Communications on Pure and Applied Mathematics. 2004 ; Vol. 57, No. 12. pp. 1627-1672.
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