Blowup phenomena of solutions to Euler–Poisson equations

✍ Scribed by Yinbin Deng; Jianlin Xiang; Tong Yang

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 191 KB
• Volume: 286
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(03)00487-6

✦ Synopsis

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.