  In this paper, we study the well-posedness for a coupled PDE/ODE system
describing the interaction of several massive point vortices moving within a
vorticity backgound in a 2D ideal incompressible fluid. The points are driven
by the velocity induced by the background vorticity, by the other vortices, and
by a Kutta-Joukowski-type lift force creating an additional gyroscopic effect.
This system reduces to the so-called vortex-wave system, introduced by
Marchioro and Pulvirenti, when the point vortices are massless. On the one
hand, we establish existence of a weak solution before the first collision. We
show moreover that the background vorticity is transported by the flow
associated to the total velocity field. On the other hand, we establish
uniqueness in the case where the vorticity is initially constant in a
neighborhood of the points vortices. When all the densities of the point
vortices have the same sign, no collision occurs in finite time and our results
are then global in time. Our proofs strongly rely on the definition of a
suitable energy functional.
