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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Analytical solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure
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by Ling Hei Yeung and Manwai Yuen PDF
Proc. Amer. Math. Soc. 139 (2011), 3951-3960 Request permission

Abstract:

We study some particular solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure, in radial symmetry. With an extension of the previous known blow-up solutions for the Euler-Poisson equations with pressureless Navier-Stokes-Poisson density-dependent viscosity, we constructed the corresponding self-similar blow-up solutions for the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure. Our solutions can provide concrete examples for testing the validation and stabilities of numerical methods for the systems.
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Additional Information
  • Ling Hei Yeung
  • Email: lightisgood2005@yahoo.com.hk
  • Manwai Yuen
  • Affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
  • Email: nevetsyuen@hotmail.com
  • Received by editor(s): September 9, 2010
  • Published electronically: April 19, 2011
  • Communicated by: Walter Craig
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3951-3960
  • MSC (2010): Primary 35B44, 35Q30, 35Q35, 85A15
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11048-7
  • MathSciNet review: 2823041