Global strong solutions to the 3D non-isentropic compressible Navier–Stokes-Poisson equations in bounded domains

This paper is concerned with initial-boundary-value problems to the 3D non-isentropic compressible Naiver-Stokes-Poisson equations, where the velocity admits slip boundary condition. For small initial energy, strong solutions are proved to exist globally in time. We overcome the difficulties caused by the domain by establishing the time-uniform higher-order norms of the absolute temperature. To this end, we first bound L 2 ( 0 , T ; L 2 ) -norm of the Poisson term, then obtain L p -norm of the gradient of the density by means of effective viscous flux. In particular, the exponential decay rate of the L 2 -norm of solutions is obtained when the absolute temperature satisfies the Dirichlet boundary condition.