  We consider the isentropic compressible Navier-Stokes-Poisson equations with
degenerate viscousities and vacuum in a three-dimensional torus. The local
well-posedness of classical solution is established by introducing a
"quasi-symmetric hyperbolic"-"degenerate elliptic" coupled structure to control
the behavior of the velocity of the fluid near the vacuum and give some uniform
estimates. In particular, the initial data allows vacuum in an open set and we
do not need any initial compatibility conditions.
