稳定彭罗斯数据附近的等离子体回波
Plasma echoes near stable Penrose data
摘要：
本文在$\mathbb{T} \times \mathbb{R}$上构造了经典Vlasov-Poisson方程组在稳定Penrose初值附近的特解，该方程组是具有任意高频率的基本波的组合.这些波相互作用，最终产生了无限级联的振幅越来越小的回声。回声解决方案不属于分析或Gevrey类研究的Mouhot和Villani，但做，尽管如此，表现出阻尼现象的大时代。
英文摘要：
In this paper we construct particular solutions to the classical Vlasov-Poisson system near stable Penrose initial data on $\mathbb{T} \times \mathbb{R}$ that are a combination of elementary waves with arbitrarily high frequencies. These waves mutually interact giving birth, eventually, to an infinite cascade of echoes of smaller and smaller amplitude. The echo solutions do not belong to the analytic or Gevrey classes studied by Mouhot and Villani, but do, nonetheless, exhibit damping phenomena for large times.
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