Sharp Decay Estimates for the Vlasov-Poisson and Vlasov-Yukawa Systems with Small Data

2019/04/12 by Xianglong Duan, Duan, Xianglong
Mathematics · #Gas Dynamics and Kinetic Theory

paper · pdf · doi:10.48550/arxiv.1904.06176

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 L¹_x,v bounds for the initial data and its derivatives. We also extend the result to the Vlasov-Yukawa system.

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