The Vlasov–Maxwell–Boltzmann System Near Maxwellians in the Whole Space with Very Soft Potentials

Since the work by Guo (Invent Math 153(3):593–630, 2003), it has remained an open problem to establish the global existence of perturbative classical solutions around a global Maxwellian to the Vlasov–Maxwell–Boltzmann system with the whole range of soft potentials. This is mainly due to the complex structure of the system, in particular, the degenerate dissipation at large velocity, the velocity-growth of the nonlinear term induced by the Lorentz force, and the regularity-loss of the electromagnetic fields. This paper solves this problem in the whole space provided that initial perturbation has sufficient regularity and velocity-integrability.