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 language | English (US) |
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Pages (from-to) | 699-716 |
Number of pages | 18 |
Journal | Moscow Mathematical Journal |
Volume | 17 |
Issue number | 4 |
DOIs | |
State | Published - Oct 1 2017 |
Externally published | Yes |
Keywords
- Area-preserving diffeomorphisms
- Casimir function
- Circulation
- Coadjoint orbit
- Enstrophy
- Hydrodynamical Euler equation
- Morse function
- Reeb graph
- Vorticity
ASJC Scopus subject areas
- General Mathematics