Asymptotic behaviour of global vortex rings

Daomin Cao; Jie Wan; Guodong Wang; Weicheng Zhan

doi:10.1088/1361-6544/ac7497

Asymptotic behaviour of global vortex rings

Daomin Cao, Jie Wan^*, Guodong Wang, Weicheng Zhan

^*Corresponding author for this work

School of Mathematics and Statistics

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

3 Citations (Scopus)

Abstract

In this paper, we are concerned with nonlinear desingularization of steady vortex rings in R3 with a general nonlinearity f. Using the improved vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in the whole space. The requirements on f are very general, and it may not satisfy the Ambrosetti-Rabinowitz condition. Some qualitative and asymptotic properties are also established.

Original language	English
Pages (from-to)	3680-3705
Number of pages	26
Journal	Nonlinearity
Volume	35
Issue number	7
DOIs	https://doi.org/10.1088/1361-6544/ac7497
Publication status	Published - 7 Jul 2022

Keywords

76B47 (35Q31)
desingularization
incompressible Euler equations
variational method
vortex ring

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10.1088/1361-6544/ac7497

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title = "Asymptotic behaviour of global vortex rings",

abstract = "In this paper, we are concerned with nonlinear desingularization of steady vortex rings in R3 with a general nonlinearity f. Using the improved vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in the whole space. The requirements on f are very general, and it may not satisfy the Ambrosetti-Rabinowitz condition. Some qualitative and asymptotic properties are also established.",

keywords = "76B47 (35Q31), desingularization, incompressible Euler equations, variational method, vortex ring",

author = "Daomin Cao and Jie Wan and Guodong Wang and Weicheng Zhan",

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T1 - Asymptotic behaviour of global vortex rings

AU - Cao, Daomin

AU - Wan, Jie

AU - Wang, Guodong

AU - Zhan, Weicheng

PY - 2022/7/7

Y1 - 2022/7/7

N2 - In this paper, we are concerned with nonlinear desingularization of steady vortex rings in R3 with a general nonlinearity f. Using the improved vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in the whole space. The requirements on f are very general, and it may not satisfy the Ambrosetti-Rabinowitz condition. Some qualitative and asymptotic properties are also established.

AB - In this paper, we are concerned with nonlinear desingularization of steady vortex rings in R3 with a general nonlinearity f. Using the improved vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in the whole space. The requirements on f are very general, and it may not satisfy the Ambrosetti-Rabinowitz condition. Some qualitative and asymptotic properties are also established.

KW - 76B47 (35Q31)

KW - desingularization

KW - incompressible Euler equations

KW - variational method

KW - vortex ring

UR - http://www.scopus.com/inward/record.url?scp=85133642368&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/ac7497

DO - 10.1088/1361-6544/ac7497

M3 - Article

AN - SCOPUS:85133642368

SN - 0951-7715

VL - 35

SP - 3680

EP - 3705

JO - Nonlinearity

JF - Nonlinearity

IS - 7

ER -

Asymptotic behaviour of global vortex rings

Abstract

Keywords

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