Bifurcation of rotating patches from kirchhoff vortices

Taoufik Hmidi; Joan Mateu

doi:10.3934/dcds.2016038

Bifurcation of rotating patches from kirchhoff vortices

Taoufik Hmidi, Joan Mateu

Mathematics

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

Abstract

In this paper we investigate the existence of a new family of rotating patches for the planar Euler equations. We shall prove the existence of countable branches bifurcating from the ellipses at some implicit angular velocities. The proof uses bifurcation tools combined with the explicit parametrization of the ellipse through the exterior conformal mappings. The boundary is shown to belong to Hölderian class.

Original language	English (US)
Pages (from-to)	5401-5422
Number of pages	22
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	10
DOIs	https://doi.org/10.3934/dcds.2016038
State	Published - Oct 2016

Keywords

Bifurcation
Kirchhoff vortices
Rotating patches

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2016038

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abstract = "In this paper we investigate the existence of a new family of rotating patches for the planar Euler equations. We shall prove the existence of countable branches bifurcating from the ellipses at some implicit angular velocities. The proof uses bifurcation tools combined with the explicit parametrization of the ellipse through the exterior conformal mappings. The boundary is shown to belong to H{\"o}lderian class.",

keywords = "Bifurcation, Kirchhoff vortices, Rotating patches",

author = "Taoufik Hmidi and Joan Mateu",

note = "Funding Information: This work was partially supported by the grants of Generalitat de Catalunya 2014SGR7, Ministerio de Economia y Competitividad MTM 2013-4469, ECPP7-Marie Curie project MAnET and the ANR project Dyficolti ANR-13-BS01-0003-01.",

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AU - Mateu, Joan

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N2 - In this paper we investigate the existence of a new family of rotating patches for the planar Euler equations. We shall prove the existence of countable branches bifurcating from the ellipses at some implicit angular velocities. The proof uses bifurcation tools combined with the explicit parametrization of the ellipse through the exterior conformal mappings. The boundary is shown to belong to Hölderian class.

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KW - Bifurcation

KW - Kirchhoff vortices

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Bifurcation of rotating patches from kirchhoff vortices

Abstract

Keywords

ASJC Scopus subject areas

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