We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along trajectories of the linearized flow. This is done by an exact integration of the linearized equation, followed by the analysis of the perturbed Hamiltonian equation in action-angle coordinates.

中文翻译：

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Vlasov-Poisson 系统点电荷的稳定性：径向情况

我们考虑具有排斥相互作用的 Vlasov-Poisson 系统。对于点电荷的小、径向、绝对连续扰动的初始数据，我们表明该解决方案是全局的，并通过沿线性化流轨迹的修改散射分散到无穷远。这是通过线性化方程的精确积分完成的，然后在动作角坐标中分析扰动的哈密顿方程。