Classification of Casimirs in 2D hydrodynamics

Understand

We describe a complete list of Casimirs for 2D Euler hydrodynamics 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.