Regularity of weak solution of the compressible Navier-Stokes equations with self-consistent Poisson equation by Moser iteration

In this paper, we consider the regularity of the weak solution to the compressible Navier-Stokes-Poisson equations in period domain $\mathrm{\Omega }\subseteq {\mathbb{R}}^3$ provided that the density $\rho (t,x)$ with integrability on the space $L^{\mathrm{\infty }}(0,T;L^{q_0}(\mathrm{\Omega }))$ where $q_0$ satisfies a certain condition and $T>0$, by which we could present that $\underset{t,x}{sup}\rho (t,x)<\mathrm{\infty }$ and $\underset{t,x}{inf}\rho (t,x)>0$. Furthermore, we develop the estimate for the velocity $\Vert u{\Vert }_{L^{\mathrm{\infty }}}$ by the Moser iteration method and Gronwall inequality.