The vortex-wave system with gyroscopic effects

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