分析和微分方程讨论班

报告题目：Nonlinear Landau Damping for the Unconfined Vlasov–Poisson System

报  告  人：Nguyen Quoc Hung（中科院数学所）

时        间：2026年10月12日(星期一），15:30-16:30

地        点：海纳苑2幢205

摘  要：We discuss nonlinear Landau damping for the Vlasov–Poisson system near the homogeneous Poisson equilibrium in two and three space dimensions. In joint work with Dongyi Wei and Zhifei Zhang, we obtained a new proof of nonlinear Landau damping and scattering in three dimensions for small, localized, neutral perturbations. We then present a two-dimensional result, obtained jointly with Alexandru D. Ionescu, establishing global classical solutions, quantitative pointwise decay of the electric field, and scattering to free transport for small, localized, neutral perturbations with weighted bounds on derivatives up to order three. The main difficulty in two dimensions is the interaction between weaker dispersion and plasma oscillations at low spatial frequencies. Our approach combines a decomposition of the electric field into regular and oscillatory components, weighted estimates for characteristics and nonlinear moments, and integration by parts in time.

联系人：王伟（wwang07@zju.edu.cn）