Abstract.
The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions isolated from incoming radiation. Various consequences of the mass-energy conservation and of the absence of incoming radiation condition are first derived assuming the existence of global smooth solutions. In the spherically symmetric case, the existence of a unique classical solution in the future of the initial cone follows by arguments similar to the case of initial data at time t=0. The total mass-energy of spherically symmetric solutions equals the (properly defined) mass-energy on backward and forward light cones.
Communicated by Sergiu Klainerman
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submitted 8/03/05, accepted 26/05/05
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Calogero, S. On a Characteristic Initial Value Problem in Plasma Physics. Ann. Henri Poincaré 7, 233–252 (2006). https://doi.org/10.1007/s00023-005-0248-2
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DOI: https://doi.org/10.1007/s00023-005-0248-2