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http://dx.doi.org/10.4134/BKMS.b170949

ON CLASSICAL SOLUTIONS AND THE CLASSICAL LIMIT OF THE VLASOV-DARWIN SYSTEM  

Li, Xiuting (School of Automatica Huazhong University of Science and Technology)
Sun, Jiamu (School of Automatica Huazhong University of Science and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.5, 2018 , pp. 1599-1619 More about this Journal
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;
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