Article
Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration
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Abstract
We study the relative equilibria in the 4-vortex problem when two of vorticities are equal to 1, and the other two equal to m are enough small. We prove that for m > 0 there is a unique concave kite relative equilibria. We also prove that there is a unique convex planar relative equilibria having two pairs of equal vorticities located at the adjacent vertices of the configuration and it is an isosceles trapezoid.
Keywords
n-vortex problem, relative equilibria, bifurcations of relative equilibria, 76F20, 37C10
Citation
Pérez-Chavela, E. & Tamayo, C. (2016). Relative equilibria in the 4-Vortex problem bifurcating from an equilateral triangle configuration. Applied Mathematics and Nonlinear Sciences, 1(1), 301–310. https://doi.org/10.21042/AMNS.2016.1.00025
E. Pérez-Chavela and C. Tamayo, “Relative equilibria in the 4-Vortex problem bifurcating from an equilateral triangle configuration,” Applied Mathematics and Nonlinear Sciences, vol. 1, no. 1, pp. 301–310, 2016, doi: 10.21042/AMNS.2016.1.00025.
Pérez-Chavela E, Tamayo C. Relative equilibria in the 4-Vortex problem bifurcating from an equilateral triangle configuration. Applied Mathematics and Nonlinear Sciences. 2016;1(1):301–310. doi:10.21042/AMNS.2016.1.00025.
Pérez-Chavela, E. and Tamayo, C. (2016), ‘Relative equilibria in the 4-Vortex problem bifurcating from an equilateral triangle configuration’, Applied Mathematics and Nonlinear Sciences, 1(1), pp. 301–310. Available at: https://doi.org/10.21042/AMNS.2016.1.00025.
Pérez-Chavela, Ernesto, and Claudia Tamayo. “Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration.” Applied Mathematics and Nonlinear Sciences, vol. 1, no. 1, 2016, pp. 301–310. https://doi.org/10.21042/AMNS.2016.1.00025.
Pérez-Chavela, Ernesto, and Claudia Tamayo. “Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration.” Applied Mathematics and Nonlinear Sciences 1, no. 1 (2016): 301–310. https://doi.org/10.21042/AMNS.2016.1.00025.
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Published by: Engineering Journals
