| Abstract: |
| In certain situations families of 2D point vortices may undergo a finite-time collapse where all vortices simultaneously converge at the same location such that their evolution cannot continue past that time. The best known scenario of this type concerns the self-similar collapse of three point vortices on the plane and was investigated by Gr{\o}bli already in 1877. We consider a quantum version of this problem where, in addition to their mutual induction, the vortices evolve under the influence of a trapping potential and argue that collapse may still occur in this setting. We propose a constructive approach based on asymptotic analysis where the collapsing configurations of quantum vortices are approximated in the limit of a weak trapping potential. It is based on a hierarchy of perturbation equations simplified using the self-similar structure of the original collapsing configuration. The collapsing configurations constructed in this manner are compared with their numerical approximations obtained by solving a multidimensional root-finding problem using a variant of Newton`s method. |
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