On classical solutions and the classical limit of the Vlasov-Darwin system
Bull. Korean Math. Soc. 2018 Vol. 55, No. 5, 1599-1619
https://doi.org/10.4134/BKMS.b170949
Published online September 30, 2018
Xiuting Li, Jiamu Sun
Huazhong University of Science and Technology, Huazhong University of Science and Technology
Abstract : 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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