Woltjer's variational principle, II: The case of unbounded domains

Peter Laurence, Marco Avellaneda

Research output: Contribution to journalArticlepeer-review


We show for a wide class of unbounded domains, that minimizing the magnetic energy subject to prescribed helicity or relative helicity, does not lead to nontrivial force-free fields. Instead, we show by an explicit construction that all minimizing sequences satisfying the helicity constraint, converge to a vacuum field.

Original languageEnglish (US)
Pages (from-to)201-241
Number of pages41
JournalGeophysical & Astrophysical Fluid Dynamics
Issue number1-4
StatePublished - Jun 1993


  • Helicity
  • lack of compactness, energy

ASJC Scopus subject areas

  • Computational Mechanics
  • Astronomy and Astrophysics
  • Geophysics
  • Mechanics of Materials
  • Geochemistry and Petrology


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