Open AccessSharp decay estimates for the Vlasov-Poisson and Vlasov-Yukawa systems with small data
Author(s) -
Xianglong Duan
Publication year - 2022
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2021049
Subject(s) - yukawa potential , dimension (graph theory) , physics , mathematical physics , vlasov equation , function (biology) , poisson distribution , plasma , mathematics , combinatorics , quantum mechanics , statistics , evolutionary biology , biology
In this paper, we present sharp decay estimates for small data solutions to 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 the bilinear terms, we improve Smulevici's result by removing the requirement of some \begin{document}$ v $\end{document} -weighted \begin{document}$ L^p $\end{document} integrability for the initial data and extend the result to the Vlasov-Yukawa system.