GLOBAL CLASSICAL SOLUTIONS AND THE CLASSICAL LIMIT OF THE NON-RELATIVISTIC VLASOV-DARWIN SYSTEM WITH SMALL INITIAL DATA  

作　　者：麻雅娴 张显文 Yaxian MA;Xianwen ZHANG(Department of Mathematics,North University of China,Taiyuan 030051,China;School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan430074,China)

机构地区：[1]Department of Mathematics,North University of China,Taiyuan 030051,China [2]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan430074,China

出　　处：《Acta Mathematica Scientia》2023年第5期2043-2060,共18页数学物理学报（B辑英文版）

基　　金：supported by the National Natural ScienceFoundation of China(11871024);the Fundamental Research Program of Shanxi Province(202103021223182)。

摘　　要：We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP)at the asymptotic rate of 1/c2 as the speed of light c tends to infinity for all time.Moreover,we obtain rigorously an asymptotic estimate of the difference between the two systems.

关 键 词：Vlasov-Darwin system generalized variables global classical solution classical limit 

分 类 号：O212.1[理学—概率论与数理统计]