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The relativistic Vlasov-Maxwell system in two space dimensions: I. II. (English) Zbl 0907.76100

Summary: A collisionless plasma is modeled by the Vlasov-Maxwell system. For the relativistic Vlasov-Maxwell system in the plane, integral representations of the electromagnetic fields are derived. Using these representations it is shown that smooth solutions can break down only if particles of the plasma approach the speed of light.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q75 PDEs in connection with relativity and gravitational theory
35Q60 PDEs in connection with optics and electromagnetic theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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