English

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 Lx,v1L^1_{x,v} 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}
}