Title: Classification of Casimirs in 2D hydrodynamics,
Abstract: 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.