论文标题
存在径向全球平滑的解决方案，用于带有二次限制的无压力Euler-Poisson方程
Existence of radial global smooth solutions to the pressureless Euler-Poisson equations with quadratic confinement
论文作者
论文摘要
我们考虑带有二次限制的无压力欧拉 - 波森方程。对于空间尺寸$ d \ ge 2，\，d \ ne 4 $，我们为存在径向全局平滑解决方案提供了必要且充分的条件，该解决方案是根据初始数据明确规定的。这种情况似乎比欧拉型方程研究中常见的关键阈值条件更加限制。为了获得我们的结果，关键的观察结果是，每个特征都满足了周期性的颂歌系统，而全球平滑解决方案的存在要求每个特征的时期都相同。
We consider the pressureless Euler-Poisson equations with quadratic confinement. For spatial dimension $d\ge 2,\,d\ne 4$, we give a necessary and sufficient condition for the existence of radial global smooth solutions, which is formulated explicitly in terms of the initial data. This condition appears to be much more restrictive than the critical-threshold conditions commonly seen in the study of Euler-type equations. To obtain our results, the key observation is that every characteristic satisfies a periodic ODE system, and the existence of global smooth solution requires the period of every characteristic to be identical.
