Classification of casimirs in 2D hydrodynamics

Anton Izosimov, Boris Khesin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We describe a complete list of Casimirs for 2D Euler hydro-dynamics on a surface without boundary: we define generalized enstrophies which, along with circulations, form a complete set of invariants for coadjoint orbits of area-preserving diffeomorphisms on a surface. We also outline a possible extension of main notions to the boundary case and formulate several open questions in that setting.

Original languageEnglish (US)
Pages (from-to)699-716
Number of pages18
JournalMoscow Mathematical Journal
Volume17
Issue number4
DOIs
StatePublished - Oct 1 2017
Externally publishedYes

Keywords

  • Area-preserving diffeomorphisms
  • Casimir function
  • Circulation
  • Coadjoint orbit
  • Enstrophy
  • Hydrodynamical Euler equation
  • Morse function
  • Reeb graph
  • Vorticity

ASJC Scopus subject areas

  • Mathematics(all)

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