Uniqueness of axisymmetric viscous flows originating from positive linear combinations of circular vortex filaments

Following the recent papers [9] and [10] by T. Gallay and V. \u{S}ver'ak, in the line of work initiated by H. Feng and V. \u{S}ver'ak in their paper [3], we prove the uniqueness of a solution of the axisymmetric Navier-Stokes equations without swirl when the initial data is a positive linear combination of Dirac masses.