Acta Applicandae Mathematicae

, Volume 153, Issue 1, pp 189–195 | Cite as

Blow-up of Smooth Solution to the Isentropic Compressible Navier-Stokes-Poisson System with Compact Density



The blow-up of smooth solution to the isentropic compressible Navier-Stokes-Poisson (NSP) system on \(\mathbb{R}^{d}\) is studied in this paper. We obtain that if the initial density is compactly supported, the spherically symmetric smooth solution to the NSP system on \(\mathbb{R}^{d}\ (d\geq 2)\) blows up in finite time. In the case \(d=1\), if \(2\mu +\lambda >0\), then the NSP system only exits a zero smooth solution on ℝ for the compactly supported initial density.


Compressible Navier-Stokes-Poisson system Smooth solution Blow-up 

Mathematics Subject Classification (2000)

76W05 35B65 35B44 



The research of B. Yuan was supported by the National Natural Science Foundation of China, Grant No. 11471103.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceHenan Polytechnic UniversityHenanChina
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenChina

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