气体星二维等温Euler-Poisson方程的解析爆破解
Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars
摘要：
研究了天体物理中描述气态星演化的欧拉-泊松方程。首先，我们构造了R^2中等温情形的一族解析爆破解。此外，还研究了上述解的爆破速率，并讨论了这些解对Navier-Stokes-Poisson方程和半导体中漂移扩散模型的适用性。最后，对于等温情形，推广了Makino和Perthame关于Tame解的结果，证明了当初始数据具有紧支集时，Tame解的寿命必定是有限的.
英文摘要：
We study the Euler-Poisson equations of describing the evolution of the gaseous star in astrophysics. Firstly, we construct a family of analytical blowup solutions for the isothermal case in R^2. Furthermore the blowup rate of the above solutions is also studied and some remarks about the applicability of such solutions to the Navier-Stokes-Poisson equations and the drift-diffusion model in semiconductors are included. Finally, for the isothermal case, the result of Makino and Perthame for the tame solutions is extended to show that the life span of such solutions must be finite if the initial data is with compact support.
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