  A kinetic-fluid model describing the evolutions of disperse two-phase flows
is considered. The model consists of the Vlasov-Fokker-Planck equation for the
particles (disperse phase) coupled with the compressible Navier-Stokes
equations for the fluid (fluid phase) through the friction force. The friction
force depends on the density, which is different from many previous studies on
kinetic-fluid models and is more physical in modeling but significantly more
difficult in analysis. New approach and techniques are introduced to deal with
the strong coupling of the fluid and the particles. The global well-posedness
of strong solution in the three-dimensional whole space is established when the
initial data is a small perturbation of some given equilibrium. Moreover, the
algebraic rate of convergence of solution toward the equilibrium state is
obtained. For the periodic domain the same global well-posedness result still
holds while the convergence rate is exponential.
