Stability of Relative Equilibria in the Planar $n$-Vortex Problem

DOI10.1137/130907434zbMath1282.70022arXiv1301.6194OpenAlexW2962689008MaRDI QIDQ2871357

Gareth E. Roberts

Publication date: 22 January 2014

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.6194

zbMATH Keywords

relative equilibrialinear stabilitynonlinear stability\(n\)-vortex problem

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Celestial mechanics (70F15) (n)-body problems (70F10) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items (21)

Periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type ⋮ Vortices on Closed Surfaces ⋮ Periodic solutions with prescribed minimal period of vortex type problems in domains ⋮ Existence and Stability of Four-Vortex Collinear Relative Equilibria with Three Equal Vorticities ⋮ Global continua of periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type ⋮ Structure and stability of the rhombus family of relative equilibria under general homogeneous forces ⋮ Relative equilibria in the four-vortex problem with two pairs of equal vorticities ⋮ Localized Spot Patterns on the Sphere for Reaction-Diffusion Systems: Theory and Open Problems ⋮ Finiteness of stationary configurations of the planar four-vortex problem ⋮ Morse theory and relative equilibria in the planar \(n\)-vortex problem ⋮ Relative periodic solutions of the \(N\)-vortex problem via the variational method ⋮ Global dynamics in a restricted five vortices problem on the plane ⋮ Stability of the rhombus vortex problem with a central vortex ⋮ Equilibria for the \(N\)-vortex-problem in a general bounded domain ⋮ Planar \(N\)-body central configurations with a homogeneous potential ⋮ Morse index and stability of the planar \(N\)-vortex problem ⋮ Periodic solutions for the N-vortex problem via a superposition principle ⋮ Stability of periodic solutions of the \(N\)-vortex problem in general domains ⋮ Influence of annular boundaries on Thomson's vortex polygon stability ⋮ Existence, Stability, and Symmetry of Relative Equilibria with a Dominant Vortex ⋮ Group scattering of point vortices on an unbounded plane

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