Optimal time-decay rates of the compressible Navier–Stokes–Poisson system in <inline-formula><tex-math id="M1">$ \mathbb R^3 $</tex-math></inline-formula>

We are concerned with the Cauchy problem of the 3D compressible Navier–Stokes–Poisson system. Compared to the previous related works, the main purpose of this paper is two–fold: First, we prove the optimal decay rates of the higher spatial derivatives of the solution. Second, we investigate the influences of the electric field on the qualitative behaviors of solution. More precisely, we show that the density and high frequency part of the momentum of the compressible Navier–Stokes–Poisson system have the same \begin{document}$ L^2 $\end{document} decay rates as the compressible Navier–Stokes equation and heat equation, but the \begin{document}$ L^2 $\end{document} decay rate of the momentum is slower due to the effect of the electric field.