Pointwise Wave--Damping for Linearized Vlasov--Poisson: Compactly Supported Radial Equilibria and Relativistic Applications
Abstract
We establish weighted pointwise estimates for the response Green function and the complete electric field of the linearized Vlasov--Poisson system in ℝx3×ℝv3 around compactly supported radial equilibria. Both decompose into a dispersive wave component with t−3/2 decay in Lx∞ 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.
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BibTeX
@misc{li2026pointwise,
title = {{Pointwise Wave--Damping for Linearized Vlasov--Poisson: Compactly Supported Radial Equilibria and Relativistic Applications}},
author = {Haina Li and Quoc-Hung Nguyen and Zhilong Xue},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26600},
eprint = {2610.26600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26600},
}
RIS
TY - UNPB
TI - Pointwise Wave--Damping for Linearized Vlasov--Poisson: Compactly Supported Radial Equilibria and Relativistic Applications
AU - Haina Li
AU - Quoc-Hung Nguyen
AU - Zhilong Xue
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26600
UR - https://arxiv.org/abs/2610.26600
AB - We establish weighted pointwise estimates for the response Green function and the complete electric field of the linearized Vlasov--Poisson system in ℝ_x^3×ℝ_v^3 around compactly supported radial equilibria. Both decompose into a dispersive wave component with t^−3/2 decay in L_x^∞ 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.
ER -