Regularity of weak solutions of compressible isentropic self-gravitating fluid

In this paper, the regularity of weak solutions to the three-dimensional compressible isentropic self-gravitating viscous fluids is considered in periodic domain. Inspired by the idea of Desjardins (1997) [3,4], we get the higher integrability of density ρ, and we remove the additional assumption of ρ∈L∞(0,T;Lq0) in the work of Choe and Jin (2003). Finally, we prove the supremum of the density is finite and the infimum of the density is positive in the domain (0,T)×T3 for a positive time T. Moreover, Moser type iteration scheme is used to obtain the L∞ norm estimate of the velocity.