Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds

Research output: Contribution to journalArticle

Abstract

Here we study the asymptotic behavior of solutions to the complex Ginzburg-Landau equations and their associated heat flows in arbitrary dimensions when the Ginzburg-Landau parameter 1/ε tends to infinity. We prove that the energies of solutions in the flow are concentrated at vortices in two dimensions, filaments in three dimensions, and codimension-2 submanifolds in higher dimensions. Moreover, we show the dynamical laws for the motion of these vortices, filaments, and codimension-2 submanifolds. Away from the energy concentration sets, we use some measure-theoretic arguments to show the strong convergence of solutions in both static and heat flow cases.

Original languageEnglish (US)
Pages (from-to)385-441
Number of pages57
JournalCommunications on Pure and Applied Mathematics
Volume51
Issue number4
DOIs
StatePublished - Apr 1998

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds'. Together they form a unique fingerprint.

  • Cite this