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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Analytical solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure


Authors: Ling Hei Yeung and Manwai Yuen
Journal: Proc. Amer. Math. Soc. 139 (2011), 3951-3960
MSC (2010): Primary 35B44, 35Q30, 35Q35, 85A15
Published electronically: April 19, 2011
MathSciNet review: 2823041
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11048-7
PII: S 0002-9939(2011)11048-7
Keywords: Fluids, Navier-Stokes-Poisson equations, density-dependent viscosity, with pressure, blowup, free boundary, self-similar solutions, global solutions, gaseous stars, semi-conductor models
Received by editor(s): September 9, 2010
Published electronically: April 19, 2011
Communicated by: Walter Craig
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.