论文标题
$ \ r^3 $的非线性Landau抑制vlasov-Poisson系统：泊松平衡
Nonlinear Landau damping for the Vlasov-Poisson system in $\R^3$: the Poisson equilibrium
论文作者
论文摘要
我们证明了euclidean空间中Vlassov-Poisson系统的解决方案之间的泊松均匀平衡的渐近稳定性$ \ Mathbb {r}^3 $。更确切地说，我们表明，泊松平衡的小，光滑和局部的扰动导致弗拉索夫 - 波桑系统的全球解决方案，该解决方案以多项式速率散布到线性溶液为$ t \ to \ to \ infty $。 我们在这里考虑的欧几里得问题与在周期性环境中的经典工作有很大不同。最重要的是，线性化的问题无法满足“ Penrose条件”。结果，我们的系统包含共振（小除差），电场是静电组件的叠加和较大的振荡组件，均具有多发腐烂的速率。
We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$. More precisely, we show that small, smooth, and localized perturbations of the Poisson equilibrium lead to global solutions of the Vlasov-Poisson system, which scatter to linear solutions at a polynomial rate as $t\to\infty$. The Euclidean problem we consider here differs significantly from the classical work on Landau damping in the periodic setting, in several ways. Most importantly, the linearized problem cannot satisfy a "Penrose condition". As a result, our system contains resonances (small divisors) and the electric field is a superposition of an electrostatic component and a larger oscillatory component, both with polynomially decaying rates.
