  In this paper we study the point-vortex dynamics with positive intensities.
We show that in the half-plane and in a disk, collapses of point-vortices with
the boundary in finite time are impossible, hence the solution of the dynamics
is global in time. We also give some necessary conditions for the existence of
collapses with the boundary in general smooth bounded domains, in particular
that the trajectory of at least one point-vortex has no limit. Some minor
results are obtained with signed intensities.
