We study compressible isentropic Navier-Stokes-Poisson equations in ℝ³. With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.

中文翻译：

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3-D 可压缩等熵 Navier-Stokes-Poisson 方程的爆破

我们研究了 ℝ ^{3 中的}可压缩等熵 Navier-Stokes-Poisson 方程。通过对密度、速度和势能的一些适当假设，我们表明具有吸引力的可压缩单极等熵 Navier-Stokes-Poisson 方程的柯西问题的经典解将在有限时间内爆炸。该证明基于矛盾论证，该论证依赖于证明总质量和总动量守恒。