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Global Behavior of Spherically Symmetric Navier–Stokes–Poisson System with Degenerate Viscosity Coefficients

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Abstract

In this paper, we study a free boundary problem for compressible spherically symmetric Navier–Stokes–Poisson equations with degenerate viscosity coefficients and without a solid core. Under certain assumptions that are imposed on the initial data, we obtain the global existence and uniqueness of the weak solution and give some uniform bounds (with respect to time) of the solution. Moreover, we obtain some stabilization rate estimates of the solution. The results show that such a system is stable under small perturbations, and could be applied to the astrophysics.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, 310027, Hangzhou, People’s Republic of China

    Ting Zhang & Daoyuan Fang

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  1. Ting Zhang
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  2. Daoyuan Fang
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Correspondence to Ting Zhang.

Additional information

This work is supported by NSFC 10571158, Zhejiang Provincial NSF of China (Y605076) and China Postdoctoral Science Foundation 20060400335.

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Zhang, T., Fang, D. Global Behavior of Spherically Symmetric Navier–Stokes–Poisson System with Degenerate Viscosity Coefficients. Arch Rational Mech Anal 191, 195–243 (2009). https://doi.org/10.1007/s00205-008-0183-8

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  • DOI: https://doi.org/10.1007/s00205-008-0183-8

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