标题： 关于非线性朗道阻尼和Gevrey正则性 显示英文标题

标题： On nonlinear Landau damping and Gevrey regularity

摘要： 在本文中，我们研究了在环面上的Vlasov-Poisson方程的非线性Landau阻尼问题。 作为我们的主要结果，我们证明了对于初始大小为$\epsilon>0$的扰动和时间区间$(0,\epsilon^{-N})$，可以在比Gevrey$3$更规则的类中得到非线性稳定性，且在$\epsilon$上一致。 作为补充结果，我们构造了显示非线性Landau阻尼的Sobolev正则初始数据族。 我们的证明基于Grenier、Nguyen和Rodnianski的方法。 显示英文摘要

摘要： In this article we study the problem of nonlinear Landau damping for the Vlasov-Poisson equations on the torus. As our main result we show that for perturbations initially of size $\epsilon>0$ and time intervals $(0,\epsilon^{-N})$ one obtains nonlinear stability in regularity classes larger than Gevrey $3$, uniformly in $\epsilon$. As a complementary result we construct families of Sobolev regular initial data which exhibit nonlinear Landau damping. Our proof is based on the methods of Grenier, Nguyen and Rodnianski.