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Diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework still remains unsolved, due to the weaker time decay rate compared with the two-species Vlasov-Maxwell-Boltzmann system. By employing the weighted energy method with two newly introduced weight functions and some novel treatments, we solve this problem for the full range of cutoff hard potentials 0 1. Uniform estimate with respect to the Knudsen number (0, 1] is established globally in time, which eventually leads to the global existence of solutions to the one-species Vlasov-Maxwell-Boltzmann system and hydrodynamic limit to the incompressible Navier-Stokes-Fourier-Maxwell system. To the best of our knowledge, this is the first result on diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework.
Wu et al. (Tue,) studied this question.