Cylindrical blowup solutions to the Isothermal Euler-Poisson Equations

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 R², 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. Copyright © 2011 American Institute of Mathematical Sciences.