  The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system
with density-dependent viscosity and drag force coefficients is investigated in
the present paper. The existence, uniqueness, and regularity of global weak
solution to the initial value problem for general initial data are established
in spatial periodic domain. Moreover, the long time behavior of the weak
solution is analyzed. It is shown that as the time grows, the distribution
function of the particles converges to the global Maxwellian, and both the
fluid velocity and the macroscopic velocity of the particles converge to the
same speed.
