Existence of small loops in a bifurcation diagram near degenerate eigenvalues

Taoufik Hmidi; Coralie Renault

doi:10.1088/1361-6544/aa82ef

Existence of small loops in a bifurcation diagram near degenerate eigenvalues

Taoufik Hmidi, Coralie Renault

Mathematics

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

Abstract

In this paper, we study the global structure of a bifurcation diagram for rotating doubly connected patches near a degenerate case for incompressible Euler equations. We show that branches with the same symmetry merge, forming a small loop, provided that they are close enough. This gives an analytical proof for the numerical observations conducted in the recent work by de la Hoz et al (2016 SIAM J. Math. Anal. 48 1892-928).

Original language	English (US)
Pages (from-to)	3821-3852
Number of pages	32
Journal	Nonlinearity
Volume	30
Issue number	10
DOIs	https://doi.org/10.1088/1361-6544/aa82ef
State	Published - Sep 15 2017

Keywords

Euler equations
bifurcation diagram
relative equilibria

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/1361-6544/aa82ef

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abstract = "In this paper, we study the global structure of a bifurcation diagram for rotating doubly connected patches near a degenerate case for incompressible Euler equations. We show that branches with the same symmetry merge, forming a small loop, provided that they are close enough. This gives an analytical proof for the numerical observations conducted in the recent work by de la Hoz et al (2016 SIAM J. Math. Anal. 48 1892-928).",

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AB - In this paper, we study the global structure of a bifurcation diagram for rotating doubly connected patches near a degenerate case for incompressible Euler equations. We show that branches with the same symmetry merge, forming a small loop, provided that they are close enough. This gives an analytical proof for the numerical observations conducted in the recent work by de la Hoz et al (2016 SIAM J. Math. Anal. 48 1892-928).

KW - Euler equations

KW - bifurcation diagram

KW - relative equilibria

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Existence of small loops in a bifurcation diagram near degenerate eigenvalues

Abstract

Keywords

ASJC Scopus subject areas

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