GLOBAL CLASSICAL SOLUTIONS FOR THE "ONE AND ONE-HALF" DIMENSIONAL RELATIVISTIC VLASOV-MAXWELL-FOKKER-PLANCK SYSTEM

In a recent paper Calogero and Alcantara [Kinet. Relat. Models, 4 (2011), pp. 401-426] derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the "one and one-half" dimensional version of this problem with nonlinear electromagnetic interactions - the relativistic Vlasov-Maxwell-Fokker-Planck system - and obtain the first results concerning well-posedness of solutions. Specifically, we prove the global-in-time existence and uniqueness of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.