New self-similar solutions of polytropic gas dynamics

@article{Lou2006NewSS,
  title={New self-similar solutions of polytropic gas dynamics},
  author={Yu-qing Lou and Wei-gang Wang and Tsinghua Center for Astrophysics and Tsinghua University and The University of Chicago and National Astronomical Observatories and Chinese Academy of Science.},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2006},
  volume={372},
  pages={885-900}
}
We explore semicomplete self-similar solutions for the polytropic gas dynamics involving self-gravity under spherical symmetry, examine behaviours of the sonic critical curve and present new asymptotic collapse solutions that describe ‘quasi-static’ asymptotic behaviours at small radii and large times. These new ‘quasi-static’ solutions with divergent mass density approaching the core can have self-similar oscillations. Earlier known solutions are summarized. Various semicomplete self-similar… 
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