Line-energy Ginzburg-Landau models: Zero-energy states

Pierre Emmanuel Jabin, Felix Otto, Benoît Perthame

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful analysis of the corresponding weak solutions by the method of characteristics.

Original languageEnglish (US)
Pages (from-to)187-202
Number of pages16
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Issue number1
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics (miscellaneous)


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