Bull. Korean Math. Soc. 2018; 55(5): 1599-1619
Online first article September 10, 2018 Printed September 30, 2018
https://doi.org/10.4134/BKMS.b170949
Copyright © The Korean Mathematical Society.
Xiuting Li, Jiamu Sun
Huazhong University of Science and Technology, Huazhong University of Science and Technology
In this paper we study the initial value problem of the non-relativistic Vlasov-Darwin system with generalized variables (VDG). We first prove local existence and uniqueness of a nonnegative classical solution to VDG in three space variables, and establish the blow-up criterion. Then we show that it converges to the well-known Vlasov-Poisson system when the light velocity $c$ tends to infinity in a pointwise sense.
Keywords: Vlasov-Darwin system, classical solution, global existence, limit
MSC numbers: Primary 35L60, 35Q83, 82D10, 85A05
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