Smoothing effects for classical solutions of the relativistic Landau–Maxwell system

The relativistic Landau–Maxwell system is one of the most fundamental and complete models for describing the dynamics of a dilute hot plasma in which particles interact through Coulomb collisions and their self-consistent electromagnetic field. In this work, we prove that the classical solutions obtained by Strain and Guo become immediately smooth with respect to all variable under the extra assumption of the electromagnetic field. As a by-product, we also prove that the classical solutions to the relativistic Landau–Poisson system and the relativistic Landau equation have the same property without any extra assumption.