Quantitative equipartition of the ginzburg-landau energy with applications

Matthias Kurzke, Daniel Spirn

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the Ginzburg-Landau energy of a single vortex and prove a quantitative estimate for the anisotropy of the stress-energy tensor. In particular we establish an asymptotic rate of equipartitioning of the energy along each direction. By means of an explicit example, this rate is shown to be optimal up to a constant. The result has applications in the study of the nonlinear wave equation and Ginzburg-Landau heat flow.

Original languageEnglish (US)
Pages (from-to)2013-2028
Number of pages16
JournalIndiana University Mathematics Journal
Volume59
Issue number6
DOIs
StatePublished - Dec 1 2010

Keywords

  • Finite epsilon estimates
  • Ginzburg-Landau energy
  • Ginzburg-Landau vortices
  • Stress-energy tensor

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