We construct solutions to the randomly-forced Navier–Stokes–Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense of probability. As such, they satisfy the system in the sense of distributions and the underlying probability space and the stochastic driving force are also unknowns of the problem. Additionally, these solutions dissipate energy, satisfies a relative energy inequality in the sense of Dafermos (1979) and satisfy a renormalized form of the continuity equation in the sense of DiPerna and Lions (1989).

中文翻译：

---

无边界域上随机强迫Navier–Stokes–Poisson系统的耗散mar解

我们在周期三维域或整个三维欧几里德空间中构造了随机作用的Navier–Stokes–Poisson系统的解。这些解决方案在PDE的意义上很弱，在概率的意义上也很弱。这样，它们在分布意义上满足了系统，并且潜在的概率空间和随机驱动力也是该问题的未知数。另外，这些解决方案耗散能量，满足Dafermos（1979）的相对能量不等式，并满足DiPerna和Lions（1989）的连续性方程的重新归一化形式。