Global solutions to the relativistic Landau–Maxwell system in the whole space

Abstract

The relativistic Landau–Maxwell system is one of the most fundamental models for description of the dynamics of dilute cold plasma in which particles interact through the Coulomb collision in the self-consistent electro-magnetic field. By constructing the compensating functions to this system and by using the structure of the equations, we obtain the global existence of classical solutions to this system in the whole space. For a simpler model, that is, the relativistic Landau–Poisson system, the analysis yields the optimal convergence rate in time to the equilibrium.