  Sprays are complex flows constituted of dispersed particles in an underlying
gas. In this paper, we are interested in the equations for moderately thick
sprays consisting of the compressible Navier-Stokes equations and Boltzmann BGK
equation. Here the coupling of two equations is through a friction (or drag)
force which depends on the density of compressible fluid and the relative
velocity between particles and fluid. For the Navier-Stokes-BGK system, we
establish the existence and uniqueness of solutions in Sobolev spaces with
exponential weight.
