Cylindrical blowup solutions to the isothermal Euler-Poisson equations

Pages: 1448 - 1456, Issue Special, September 2011

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Manwai Yuen - Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China (email)

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.

Keywords:  Analytical solutions, Euler-Poisson equations, isothermal, blowup, global solutions, classical solutions, cylindrical, star formation, $R^N$
Mathematics Subject Classification:  Primary: 35Q85 85A15; Secondary: 35B44, 35Q30, 35Q35, 85A05

Received: June 2010;      Revised: February 2011;      Published: October 2011.