Pointwise Wave--Damping for Linearized Vlasov--Poisson: Compactly Supported Radial Equilibria and Relativistic Applications
Year: 2026
Type: preprint
Abstract: We establish weighted pointwise estimates for the response Green function and the complete electric field of the linearized Vlasov--Poisson system in $\mathbb{R}_x^3\times\mathbb{R}_v^3$ around compactly supported radial equilibria. Both decompose into a dispersive wave component with $t^{-3/2}$ decay in $L_x^\infty$ and a faster-decaying Landau-damped component. The wave estimate includes the survival threshold, where the oscillatory branch meets the continuous spectrum, while the damped estimates resolve the spatial fronts associated with the velocity boundaries. The equilibrium class includes shells with independent inner and outer orders of vanishing, down to first order, and profiles positive throughout a velocity ball. The proof combines a joint treatment of pole and continuum contributions with a low-frequency normal form for the electric field. The electric-field estimates hold for real, neutral perturbations with finite weighted regularity and imply uniform scattering along free characteristics. An exact momentum--velocity correspondence for suitable filled-ball profiles yields analogous estimates and scattering for a class of nonnegative relativistic equilibria with polynomial momentum tails.
Source: arXiv (Cornell University)
Authors: Li, Haina, Nguyen, Quoc-Hung, Xue, Zhilong
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5053629486
OpenAlex ID: W7223044253