Stability in 2D ginzburg-landau passes to the limit

Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

We prove that if we consider a family of stable solutions to the Ginzburg-Landau equation, then their vortices converge to a stable critical point of the "renormalized energy." Moreover, in the case of instability, the number of "directions of descent" is bounded below by the number of directions of descent for the renormalized energy. A consequence is a result of nonexistence of stable nonconstant solutions to Ginzburg-Landau with homogeneous Neumann boundary condition.

Original languageEnglish (US)
Pages (from-to)199-222
Number of pages24
JournalIndiana University Mathematics Journal
Volume54
Issue number1
DOIs
StatePublished - 2005

Keywords

  • Asymptotics
  • Ginzburg-Landau
  • Stability
  • Vortices

ASJC Scopus subject areas

  • Mathematics(all)

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