发表机构
Princeton University; Academy of Mathematics and Systems Science, Chinese Academy of Sciences（普林斯顿大学; 中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文证明了二维无约束Vlasov-Poisson系统在均匀平衡附近的非线性Landau阻尼，建立了全局存在性、电场衰减估计及散射结果，是首个此类结果。
AI 中文摘要
我们证明了在无约束欧几里得空间中，二维Vlasov-Poisson系统在均匀Poisson平衡μ(v)=1/(2π)(1+|v|^2)^{-3/2}附近的非线性Landau阻尼。对于小、光滑、局部化且中性的扰动，我们建立了全局存在性、电场定量逐点衰减估计以及散射到自由输运。我们在此证明的结果似乎是针对无约束二维Vlasov-Poisson系统解的首个非线性Landau阻尼结果。均匀Penrose稳定性界在低空间频率处退化，导致弱阻尼等离子体振荡。我们将衰减更快的正则场与具有时间因子cos(t)和sin(t)的振荡分量分离。证明结合了密度的Volterra表示、特征流和非线性矩的加权估计以及时间上的分部积分。中性条件提供了临界二维估计中所需的空间抵消。
英文摘要
We prove nonlinear Landau damping for the two-dimensional Vlasov--Poisson system in the unconfined Euclidean setting near the homogeneous Poisson equilibrium \[ μ(v)=\frac{1}{2π}(1+|v|^2)^{-3/2}. \] For small, smooth, localized, and neutral perturbations we establish global existence, quantitative pointwise decay estimates for the electric field, and scattering to free transport. The result we prove here appears to be the first nonlinear Landau damping result for solution of the unconfined 2D Vlasov--Poisson system. The uniform Penrose stability bound degenerates at low spatial frequencies, giving rise to weakly damped plasma oscillations. We separate a faster-decaying regular field from oscillatory components with temporal factors $\cos(t)$ and $\sin(t)$. The proof combines a Volterra representation of the density, weighted estimates for the characteristic flow and nonlinear moments, and integration by parts in time. Neutrality supplies the spatial cancellation needed in the critical two-dimensional estimates.
Comments73 pages
