Compactness and stability for planar vortex-pairs with prescribed impulse

Research output: Contribution to journalArticle

Abstract

Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the constraint set comprises the set of all equimeasurable rearrangements of a given function (representing vorticity) that have a prescribed impulse (linear momentum). A form of orbital stability is deduced.

Original languageEnglish
Pages (from-to)547-572
Number of pages26
JournalJournal of Differential Equations
Volume270
Early online date15 Sep 2020
DOIs
Publication statusE-pub ahead of print - 15 Sep 2020

Keywords

  • Compactness
  • Convexity
  • Maximiser
  • Rearrangements
  • Stability
  • Vortex

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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