Abstract：In this talk，we are interested in long time dynamics of 3 dimensional Navier-Stokes-Poisson（NSP） system near a stationary solution（\rho，u）＝（1，0）. In fact， there are many references about this question. But all the positive results up to now need the assumption that initial perturbation is small proportional to rescaled parameter （\varepsilon）. On the other hand，when \varepsilon is taken to be 0， that is for Euler -Poisson system ，it has been proved by Guo that there are global existence，under small irrotational neutral initial perturbation. The irrotational assumption here seems optimal. In this talk，we will combine these two results to prove that there are also global existence for NSP system in some high order Sobolev space if the curl-free part of initial velocity perturbation is small proportional to \varepsilon while the other parts of initial perturbation is small but can be taken independent of \varepsilon. We hope that our ideas presented here can be useful to other viscous system （such as Navier-Stokes-Kortweg， free surface Navier-Stokes system with gravity ) where the corresponding inviscid system admits global solutions.
