Existence of helical symmetry vortex patch with small cross-section for the incompressible Euler equations in R3

Daomin Cao; Rui Li; Guolin Qin; Jie Wan

doi:10.1016/j.jde.2024.11.044

Existence of helical symmetry vortex patch with small cross-section for the incompressible Euler equations in R³

Daomin Cao
, Rui Li^*
, Guolin Qin
, Jie Wan

^*Corresponding author for this work

School of Mathematics and Statistics

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

Abstract

In this paper, we construct a family of traveling-rotating helical symmetry vortex patches to the incompressible Euler equations in R³, which tend asymptotically to singular helical vortex filament evolving by the binormal curvature flow. The construction is achieved by maximizing the energy functional over certain constraint and studying carefully asymptotic behavior of maximizers.

Original language	English
Pages (from-to)	459-495
Number of pages	37
Journal	Journal of Differential Equations
Volume	418
DOIs	https://doi.org/10.1016/j.jde.2024.11.044
Publication status	Published - 15 Feb 2025

Keywords

Helical symmetry vortex
Incompressible Euler equation
Patch type solutions
Variational methods

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10.1016/j.jde.2024.11.044

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title = "Existence of helical symmetry vortex patch with small cross-section for the incompressible Euler equations in R3",

abstract = "In this paper, we construct a family of traveling-rotating helical symmetry vortex patches to the incompressible Euler equations in R3, which tend asymptotically to singular helical vortex filament evolving by the binormal curvature flow. The construction is achieved by maximizing the energy functional over certain constraint and studying carefully asymptotic behavior of maximizers.",

keywords = "Helical symmetry vortex, Incompressible Euler equation, Patch type solutions, Variational methods",

author = "Daomin Cao and Rui Li and Guolin Qin and Jie Wan",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2025",

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day = "15",

doi = "10.1016/j.jde.2024.11.044",

language = "English",

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T1 - Existence of helical symmetry vortex patch with small cross-section for the incompressible Euler equations in R3

AU - Cao, Daomin

AU - Li, Rui

AU - Qin, Guolin

AU - Wan, Jie

PY - 2025/2/15

Y1 - 2025/2/15

N2 - In this paper, we construct a family of traveling-rotating helical symmetry vortex patches to the incompressible Euler equations in R3, which tend asymptotically to singular helical vortex filament evolving by the binormal curvature flow. The construction is achieved by maximizing the energy functional over certain constraint and studying carefully asymptotic behavior of maximizers.

AB - In this paper, we construct a family of traveling-rotating helical symmetry vortex patches to the incompressible Euler equations in R3, which tend asymptotically to singular helical vortex filament evolving by the binormal curvature flow. The construction is achieved by maximizing the energy functional over certain constraint and studying carefully asymptotic behavior of maximizers.

KW - Helical symmetry vortex

KW - Incompressible Euler equation

KW - Patch type solutions

KW - Variational methods

UR - https://www.scopus.com/pages/publications/85210988792

U2 - 10.1016/j.jde.2024.11.044

DO - 10.1016/j.jde.2024.11.044

M3 - Article

AN - SCOPUS:85210988792

SN - 0022-0396

VL - 418

SP - 459

EP - 495

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Existence of helical symmetry vortex patch with small cross-section for the incompressible Euler equations in R³

Abstract

Keywords

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