Steady asymmetric vortex pairs for Euler equations

Zineb Hassainia; Taoufik Hmidi

doi:10.3934/dcds.2020348

Steady asymmetric vortex pairs for Euler equations

Zineb Hassainia, Taoufik Hmidi

Mathematics

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

Abstract

In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.

Original language	English (US)
Pages (from-to)	1939-1969
Number of pages	31
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	41
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2020348
State	Published - Apr 2021

Keywords

Desingularization
Euler equations
Implicit function theorem
Steady vortex pairs
Vortex dynamics

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcds.2020348

Cite this

@article{e252277693cb48d8b3586f899b9ea8b4,

title = "Steady asymmetric vortex pairs for Euler equations",

abstract = "In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.",

keywords = "Desingularization, Euler equations, Implicit function theorem, Steady vortex pairs, Vortex dynamics",

author = "Zineb Hassainia and Taoufik Hmidi",

year = "2021",

month = apr,

doi = "10.3934/dcds.2020348",

language = "English (US)",

volume = "41",

pages = "1939--1969",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "4",

}

TY - JOUR

T1 - Steady asymmetric vortex pairs for Euler equations

AU - Hassainia, Zineb

AU - Hmidi, Taoufik

PY - 2021/4

Y1 - 2021/4

N2 - In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.

AB - In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.

KW - Desingularization

KW - Euler equations

KW - Implicit function theorem

KW - Steady vortex pairs

KW - Vortex dynamics

UR - http://www.scopus.com/inward/record.url?scp=85101179011&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85101179011&partnerID=8YFLogxK

U2 - 10.3934/dcds.2020348

DO - 10.3934/dcds.2020348

M3 - Article

AN - SCOPUS:85101179011

SN - 1078-0947

VL - 41

SP - 1939

EP - 1969

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

ER -

Steady asymmetric vortex pairs for Euler equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this