Classification of casimirs in 2D hydrodynamics

Anton Izosimov; Boris Khesin

doi:10.17323/1609-4514-2017-17-4-699-716

Classification of casimirs in 2D hydrodynamics

Anton Izosimov
, Boris Khesin

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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)
Pages (from-to)	699-716
Number of pages	18
Journal	Moscow Mathematical Journal
Volume	17
Issue number	4
DOIs	https://doi.org/10.17323/1609-4514-2017-17-4-699-716
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

Access to Document

10.17323/1609-4514-2017-17-4-699-716

Cite this

@article{f06d22f1b18b4e829a7721bed7263f4a,

title = "Classification of casimirs in 2D hydrodynamics",

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.",

keywords = "Area-preserving diffeomorphisms, Casimir function, Circulation, Coadjoint orbit, Enstrophy, Hydrodynamical Euler equation, Morse function, Reeb graph, Vorticity",

author = "Anton Izosimov and Boris Khesin",

note = "Publisher Copyright: {\textcopyright} 2017 Independent University of Moscow.",

year = "2017",

month = oct,

day = "1",

doi = "10.17323/1609-4514-2017-17-4-699-716",

language = "English (US)",

volume = "17",

pages = "699--716",

journal = "Moscow Mathematical Journal",

issn = "1609-3321",

publisher = "Independent University of Moscow",

number = "4",

}

TY - JOUR

T1 - Classification of casimirs in 2D hydrodynamics

AU - Izosimov, Anton

AU - Khesin, Boris

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Area-preserving diffeomorphisms

KW - Casimir function

KW - Circulation

KW - Coadjoint orbit

KW - Enstrophy

KW - Hydrodynamical Euler equation

KW - Morse function

KW - Reeb graph

KW - Vorticity

UR - https://www.scopus.com/pages/publications/85036496858

UR - https://www.scopus.com/pages/publications/85036496858#tab=citedBy

U2 - 10.17323/1609-4514-2017-17-4-699-716

DO - 10.17323/1609-4514-2017-17-4-699-716

M3 - Article

AN - SCOPUS:85036496858

SN - 1609-3321

VL - 17

SP - 699

EP - 716

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 4

ER -

Classification of casimirs in 2D hydrodynamics

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this