Cylindrical blowup solutions to the isothermal Euler-Poisson equations

Manwai Yuen

doi:10.3934/proc.2011.2011.1448

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2011, Volume 2011: 1448-1456. Doi: 10.3934/proc.2011.2011.1448 open access

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Cylindrical blowup solutions to the isothermal Euler-Poisson equations

Manwai Yuen^1,

1.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: May 31, 2010

Revised: January 31, 2011

Published: August 2017

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Abstract

This proceeding is the continued version of the analytical blowup solutions for 2-dimensional Euler-Poisson equations in ”M.W. Yuen, Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars, J. Math. Anal. Appl. 341 (2008), 445–456”. With the extension of the blowup solutions with radial symmetry for the isothermal Euler-Poisson equations in R$^2$, the cylindrical blowup solutions in R$^N$ ($N>=3$) with are constructed by the separation method. Here, the constructed 3-dimensional blowup solutions could be applied to interpret the evolution of cylindrical cloud for star formation in astrophysics.

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Mathematics Subject Classification: Primary: 35Q85 85A15; Secondary: 35B44, 35Q30, 35Q35, 85A05.

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Cylindrical blowup solutions to the isothermal Euler-Poisson equations

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