Blowup phenomena of solutions to Euler–Poisson equations

AbstractIn 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 RN, 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