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On classical solutions and the classical limit of the Vlasov-Darwin system
Xiuting Li,Jiamu Sun 대한수학회 2018 대한수학회보 Vol.55 No.5
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.
ON CLASSICAL SOLUTIONS AND THE CLASSICAL LIMIT OF THE VLASOV-DARWIN SYSTEM
Li, Xiuting,Sun, Jiamu Korean Mathematical Society 2018 대한수학회보 Vol.55 No.5
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.