Large-time behavior of the two-species relativistic Landau–Maxwell system in Rx3

We study the optimal time-decay and the L2L2-stability of classical solutions to the two-species relativistic Landau–Maxwell system in the whole space Rx3. The global existence of this system has been established by Yang and Yu [34] in the perturbative regime of global Maxwellian. Based on our previous works on the optimal time-decay for the Vlasov–Poisson–Boltzmann system, we prove that for this system and its simpler model, the relativistic Landau–Poisson system, every order derivative of the solutions converges to the global Maxwellian at an optimal time decay rate. Moreover, the uniform L2L2-stability of the solutions in Yang and Yu [34] is also provided.