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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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:
  • Manwai Yuen
  • Affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
  • Email:
  • 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:
  • MathSciNet review: 2823041