  We analyze the Vlasov equation coupled with the compressible Navier--Stokes
equations with degenerate viscosities and vacuum. These two equations are
coupled through the drag force which depends on the fluid density and the
relative velocity between particle and fluid. We first establish the existence
and uniqueness of local-in-time regular solutions with arbitrarily large
initial data and a vacuum. We then present sufficient conditions on the initial
data leading to the finite-time blowup of regular solutions. In particular, our
study makes the result on the finite-time singularity formation for
Vlasov/Navier-Stokes equations discussed by Choi [J. Math. Pures Appl., 108,
(2017), 991-1021] completely rigorous.
