  In this paper we introduce a PDE system which aims at describing the dynamics
of a dispersed phase of particles moving into an incompressible perfect fluid,
in two space dimensions. The system couples a Vlasov-type equation and an
Euler-type equation: the fluid acts on the dispersed phase through a gyroscopic
force whereas the latter contributes to the vorticity of the former.
  First we give a Dobrushin type derivation of the system as a mean-field limit
of a PDE system which describes the dynamics of a finite number of massive
pointwise particles moving into an incompressible perfect fluid.
  This last system is itself inferred from a joint work of the second author
with O. Glass and C. Lacave, where the system for one massive pointwise
particle was derived as the limit of the motion of a solid body when the body
shrinks to a point with fixed mass and circulation.
  Then we deal with the well-posedness issues including the existence of weak
solutions. Next we exhibit the Hamiltonian structure of the system and finally,
we study the behavior of the system in the limit where the mass of the
particles vanishes.
