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- W2012045685 abstract "The relativistic Vlasov-Darwin system is an approximation of the Vlasov-Maxwell system when particles velocities are not too fast when compared with the speed of light. The main difficulty when dealing with this system stems from the fact that the energy conservation law does not give any control over a part of the electric field; as a result, global-in-time weak solutions were known to exist only in the case of small initial data. Here we remove the smallness assumption to establish the existence of global-in-time weak solutions for general initial data. Also, we prove the existence of a unique local-in-time strong solution for smooth data, which seems to be the first result of its kind for the system under consideration." @default.
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- W2012045685 date "2006-01-01" @default.
- W2012045685 modified "2023-09-26" @default.
- W2012045685 title "The initial value problem for the relativistic Vlasov-Darwin system" @default.
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- W2012045685 doi "https://doi.org/10.1155/imrn/2006/57191" @default.
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