排斥型Euler-Poisson方程多维轴对称解的性态
On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations
摘要：
本文证明了冷等离子体振荡所对应的非零背景下的排斥Euler-Poisson方程的径向对称解在除了$\bd=4$以外的许多空间维度上几乎对所有的初始数据都是爆破的。初始数据对应于简单波，其解可能不会爆炸。此外，如果一个解在时间上是全局光滑的，那么它要么是仿射的，要么倾向于仿射为$t\to\infty$。
英文摘要：
It is proved that the radially symmetric solutions of the repulsive Euler-Poisson equations with a non-zero background, corresponding to cold plasma oscillations blow up in many spatial dimensions except for $\bd=4$ for almost all initial data. The initial data, for which the solution may not blow up, correspond to simple waves. Moreover, if a solution is globally smooth in time, then it is either affine or tends to affine as $t\to\infty$.
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