Blowup phenomena of solutions to Euler-Poisson equations

In this paper, we consider the Euler-Poisson equations governing the evolution of the gaseous stars with the Poisson equation describing the energy potential for the self-gravitating force. By assuming that the initial density is of compact support in R^N, we first give a family of blowup solutions for non-isentropic polytropic gas when γ = (2N - 2)/N which generalizes the known result for the isentropic case. Then we extend the previous result on non-blowup phenomena to the case when (2N - 2)/N ≤ γ <2 in N-dimensional space. Here γ is the adiabatic gas constant. © 2003 Elsevier Inc. All rights reserved.