A collisionless plasma is modeled by the Vlasov–Poisson system. Smooth solutions are considered in three spatial dimensions with compactly supported initial data. The main theorem of this work is a small data result that improves an earlier theorem of Bardos and Degond in that it does not require the derivatives of the initial data to be small. Another theorem is presented here that gives a sufficient condition that ensures that the charge density decays as $t^{-3}$, which is the rate which occurs when asymptotically all particles disperse freely.

中文翻译：

---

Vlasov-Poisson系统的改进的小数据定理

无碰撞等离子体由Vlasov-Poisson系统建模。在具有紧凑支持的初始数据的三个空间维度上考虑了光滑解。这项工作的主要定理是小数据结果，它改进了Bardos和Degond的早期定理，因为它不需要初始数据的导数要小。此处给出另一个定理，该定理给出了一个足以确保电荷密度随$ t ^ {-3} $衰减的条件，这是渐近所有粒子自由分散时发生的速率。