The ''two and one-half dimensional'' relativistic Vlasov Maxwell system

The motion of a collisionless plasma is modelled by solutions to the Vlasov-Maxwell system. The Cauchy problem for the relativistic Vlasov-Maxwell system is studied in the case when the phase space distribution function f = f(t, x, v) depends on the time t, x epsilon R-2 and v epsilon R-3. Global existence of classical solutions is obtained for smooth data of unrestricted size. A sufficient condition for global smooth solvability is known from [12]: smooth solutions can break down only if particles of the plasma approach the speed of light. An a priori bound is obtained on the velocity support of the distribution function, from which the result follows.