Well-posedness of classical solutions to the 3D isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities and vacuum

We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities 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.