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Stability of the Rhombus Vortex Problem with a Central Vortex

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Abstract

We characterize the type stability of the five-vortex problem in the plane, where it is assumed that configuration is a rhombus vortex problem with a central vortex. More precisely, we suppose that the opposite vortices have the same vorticity \(\Gamma _1=\Gamma _2=1\) and \(\Gamma _3=\Gamma _4=\Gamma \ne 0\) and the vortex at the center has vorticity \(\Gamma _0\ne 0\). The stability is given in terms of the size of the rhombus and the vorticities.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Sergipe, Aracaju, Brazil

    Allyson Oliveira

  2. Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5–C, Concepción, VIII–Región, Chile

    Claudio Vidal

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  1. Allyson Oliveira
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  2. Claudio Vidal
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Correspondence to Allyson Oliveira.

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Oliveira, A., Vidal, C. Stability of the Rhombus Vortex Problem with a Central Vortex. J Dyn Diff Equat 32, 2109–2123 (2020). https://doi.org/10.1007/s10884-019-09805-7

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