Classification of Casimirs in 2D hydrodynamics
Symplectic Geometry
2017-03-14 v2 Mathematical Physics
math.MP
Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.1702.01843,
title = {Classification of Casimirs in 2D hydrodynamics},
author = {Anton Izosimov and Boris Khesin},
journal= {arXiv preprint arXiv:1702.01843},
year = {2017}
}
Comments
17 pages, 5 figures