CLASSIFICATION OF CASIMIRS IN 2D HYDRODYNAMICS

被引：8
|
作者：
Izosimov, Anton [1 ]
Khesin, Boris [1 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M58 2E4, Canada
来源：
MOSCOW MATHEMATICAL JOURNAL | 2017年 / 17卷 / 04期
关键词：
Area-preserving diffeomorphisms; enstrophy; Casimir function; coadjoint orbit; vorticity; circulation; hydrodynamical ruler equation; Reelb graph; Morse function;
D O I：
10.17323/1609-4514-2017-17-4-699-716
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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收藏
页码：699 / 716
页数：18
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