LAUSR

The blow-up of smooth solution to the isentropic compressible Navier-Stokes-Poisson (NSP) system on Rd$\mathbb{R}^{d}$ is studied in this paper. We obtain that if the initial density is compactly supported, the spherically symmetric smooth solution to the NSP system on Rd(d≥2)$\mathbb{R}^{d}\ (d\geq 2)$ blows up in finite time. In the case d=1$d=1$, if 2μ+λ>0$2\mu +\lambda >0$, then the NSP system only exits a zero smooth solution on ℝ for the compactly supported initial density.