We prove a stability result of constant equilibria for the three dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity to be small independently of the rescaled viscosity parameter ε while the incompressible part of the initial velocity is assumed to be small compared to ε. We then get a unique global smooth solution. We also prove a uniform in ε time decay rate for these solutions. Our approach allows to combine the parabolic energy estimates that are efficient for the viscous equation at ε fixed and the dispersive techniques (dispersive estimates and normal forms) that are useful for the inviscid irrotational system.

我们证明了在无粘性极限下均匀的三维 Navier-Stokes-Poisson 系统的恒定平衡的稳定性结果。我们允许初始密度接近常数，初始速度的潜在部分与重新缩放的粘度参数ε无关，而初始速度的不可压缩部分假设与ε相比较小。然后我们得到一个独特的全局平滑解。我们还证明了这些解的ε时间衰减率是一致的。我们的方法允许结合对ε处的粘性方程有效的抛物线能量估计 固定和色散技术（色散估计和标准形式）对无粘性无旋系统有用。