  In this paper, the system of particles coupled with fluid is considered. The
particles are described by a Vlasov equation, and the fluid is governed by a
forced Navier-Stokes equations. The interaction with fluid phase governed by
Navier-Stokes equations is taken into account through a source term. The
resulting system, namely Navier-Stokes-Vlasov equations, is shown to have
global weak solutions in three spatial dimensions, and to have a unique global
solution in two spatial dimensions.
