  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.
