On the onset of filamentation on two-dimensional vorticity interfaces

Adrian Constantin; David Dritschel; Pierre Germain

doi:10.1088/1361-6544/adf16b

On the onset of filamentation on two-dimensional vorticity interfaces

Adrian Constantin, David Dritschel, Pierre Germain^*

^*Corresponding author for this work

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

Abstract

We study an asymptotic nonlinear model for filamention on two-dimensional vorticity interfaces. Different re-formulations of the model equation reveal its underlying structural properties. They enable us to construct global weak solutions and to prove the existence of traveling waves.

Original language	English
Article number	085018
Number of pages	16
Journal	Nonlinearity
Volume	38
Issue number	8
DOIs	https://doi.org/10.1088/1361-6544/adf16b
Publication status	Published - 22 Aug 2025

Keywords

Nonlinear wave
Filamentation
Vortex patch
Weak solutions
Solitary waves

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Constantin_2025_Nonlinearity_On-onset-filamentation-2D-vorticity-interfaces_CC
© 2025 The Author(s). Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license (https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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Cite this

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title = "On the onset of filamentation on two-dimensional vorticity interfaces",

abstract = "We study an asymptotic nonlinear model for filamention on two-dimensional vorticity interfaces. Different re-formulations of the model equation reveal its underlying structural properties. They enable us to construct global weak solutions and to prove the existence of traveling waves.",

keywords = "Nonlinear wave, Filamentation, Vortex patch, Weak solutions, Solitary waves",

author = "Adrian Constantin and David Dritschel and Pierre Germain",

note = "Funding: Adrian Constantin was supported by the Austrian Science Fund (FWF), grant number Z 387-N. Pierre Germain was supported by a Wolfson fellowship from the Royal Society and the Simons collaboration on Wave Turbulence.",

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AU - Constantin, Adrian

AU - Dritschel, David

AU - Germain, Pierre

N1 - Funding: Adrian Constantin was supported by the Austrian Science Fund (FWF), grant number Z 387-N. Pierre Germain was supported by a Wolfson fellowship from the Royal Society and the Simons collaboration on Wave Turbulence.

PY - 2025/8/22

Y1 - 2025/8/22

N2 - We study an asymptotic nonlinear model for filamention on two-dimensional vorticity interfaces. Different re-formulations of the model equation reveal its underlying structural properties. They enable us to construct global weak solutions and to prove the existence of traveling waves.

AB - We study an asymptotic nonlinear model for filamention on two-dimensional vorticity interfaces. Different re-formulations of the model equation reveal its underlying structural properties. They enable us to construct global weak solutions and to prove the existence of traveling waves.

KW - Nonlinear wave

KW - Filamentation

KW - Vortex patch

KW - Weak solutions

KW - Solitary waves

UR - https://www.scopus.com/pages/publications/105013879462

U2 - 10.1088/1361-6544/adf16b

DO - 10.1088/1361-6544/adf16b

M3 - Article

SN - 0951-7715

VL - 38

JO - Nonlinearity

JF - Nonlinearity

IS - 8

M1 - 085018

ER -

On the onset of filamentation on two-dimensional vorticity interfaces

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Keywords

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