论文标题
关于排斥Euler-Poisson方程的多维轴对称解的行为
On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations
论文作者
论文摘要
事实证明，具有非零背景的排斥Euler-poisson方程的径向对称解，对应于许多空间维度的冷等离子体振荡，除了$ \ bd = 4 $，几乎所有初始数据。解决方案可能不会爆炸的初始数据对应于简单的波。此外，如果解决方案在全球范围内保持光滑，则它是仿射或倾向于仿射为$ t \ to \ infty $。
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 $t\to\infty$.
