Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy

We study the low-energy solutions to the 3D compressible NavierStokes-Poisson equations. We first obtain the existence of smooth solutions with small L²-norm and essentially bounded densities. No smallness assumption is imposed on the H⁴-norm of the initial data. Using a compactness argument, we further obtain the existence of weak solutions which may have discontinuities across some hypersurfaces in R³. We also provide a blow-up criterion of solutions in terms of the L^∞-norm of density. Copyright © 2019 American Institute of Mathematical Sciences.