We will show the blow-up of smooth solutions to the Cauchy problems for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing and compressible bipolar isentropic Navier-Stokes-Poisson equations in arbitrary dimensions under some restrictions on the initial data. The key of the proof is finding the relations between the physical quantities and establishing some differential inequalities.

中文翻译：

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可压缩等熵 Navier-Stokes-Poisson 方程的爆破

我们将展示可压缩单极等熵 Navier-Stokes-Poisson 方程的 Cauchy 问题的平滑解的爆炸，该方程具有任意维度的吸引力强迫和可压缩双极等熵 Navier-Stokes-Poisson 方程，在初始数据的一些限制下。证明的关键是找出物理量之间的关系并建立一些微分不等式。