| Abstract: |
| Point vortices in a plane form a dynamical system introduced by Helmholtz in 1858. A vortex equilibrium according to O`Neil is a solution where all vortices move with a common velocity, where the configuration formed by the vortices is stationary or translating depending on whether the velocity is zero or not.
In this talk, we will present some results of the enumeration problems for $n$-vortex translating configurations and $n$-vortex stationary configurations. Especially, for $n\geq 4$, we will show there exist circulations yielding no translating configurations. Similarly, for $n\geq 5$, there are circulations yielding no stationary configurations. Then, such circulations satisfying the necessary conditions for vortex equilibria but yielding no vortex equilibria will be generalized. |
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