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

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

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...

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Veröffentlicht in:Taehan Suhakhoe hoebo 2018, Vol.55 (5), p.1599-1619
Hauptverfasser: Li, Xiuting, Sun, Jiamu
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description 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.
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