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In a recent paper Calogero and Alcantara derived a Lorentz-invariantFokker-Planck equation, which corresponds to the evolution of a particledistribution associated with relativistic Brownian Motion. We study the "oneand one-half" dimensional version of this problem with nonlinearelectromagnetic interactions - the relativistic Vlasov-Maxwell-Fokker-Plancksystem - and obtain the first results concerning well-posedness of solutions.Specifically, we prove the global-in-time existence and uniqueness of classicalsolutions to the Cauchy problem and a gain in regularity of the distributionfunction in its momentum argument.

Global Existence for the "One and one-half" dimensional relativistic Vlasov-Maxwell-Fokker-Planck system