Sharp Decay Estimates for the Vlasov-Poisson and Vlasov-Yukawa Systems with Small Data
Analysis of PDEs
2019-04-15 v1
Abstract
In this paper, we present sharp decay estimates for small data solutions of the following two systems: the Vlasov-Poisson (V-P) system in dimension 3 or higher and the Vlasov-Yukawa (V-Y) system in dimension 2 or higher. We rely on a modification of the vector field method for transport equation as developed by Smulevici in 2016 for the Vlasov-Poisson system. Using the Green's function in particular to estimate bilinear terms, we improve Smulevici's result by requiring only bounds for the initial data and its derivatives. We also extend the result to the Vlasov-Yukawa system.
Keywords
Cite
@article{arxiv.1904.06176,
title = {Sharp Decay Estimates for the Vlasov-Poisson and Vlasov-Yukawa Systems with Small Data},
author = {Xianglong Duan},
journal= {arXiv preprint arXiv:1904.06176},
year = {2019}
}