Global Well-posedness of Classical Solutions to the Compressible Navier-Stokes-Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains

Abstract: We consider the initial-boundary-value problem of the isentropic compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile in 3D bounded domain with slip boundary condition and vacuum. The global well-posedness of classical solution is established with small initial energy but possibly large oscillations and vacuum. The steady state (except velocity) and the doping profile are allowed to be of large variation.