Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain (Q606051)

The authors examine the stability of the Thomson vortex polygon with evenly many vortices outside a circular domain. The authors first provide the equations of motion for \(n\) point vortices outside a circular domain and find their integrals and symmetry groups. Then, the authors study the stability of stationary rotation of regular vortex polygon outside the circular domain. The authors justify the linearization method for \(n = 2, 4, 6\) and \(n\geqq 7\), and prove the instability of the steady rotation of vortex polygon in the critical case and for \(n = 2,4, 6\).