Abstract
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.
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Acknowledgement
The research of B. Yuan was supported by the National Natural Science Foundation of China, Grant No. 11471103.
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Yuan, B., Zhao, X. Blow-up of Smooth Solution to the Isentropic Compressible Navier-Stokes-Poisson System with Compact Density. Acta Appl Math 153, 189–195 (2018). https://doi.org/10.1007/s10440-017-0127-0
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DOI: https://doi.org/10.1007/s10440-017-0127-0