In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space @math when the positive charged ion flow provides a spatially uniform background. The most key point of studying this coupled degenerately dissipative system here is to establish the dissipation of the electromagnetic field which turns out to be of the regularity-loss type. Precisely, for the linearized non-homogeneous system, some @math energy functionals and @math time-frequency functionals which are equivalent with the naturally existing ones are designed to capture the optimal dissipation rate of the system, which in turn yields the optimal @math - @math type time-decay estimates of the corresponding linearized solution operator. These results show a special feature of the one-species Vlasov-Maxwell-Boltzmann system different from the case of two-species, that is, the dissipation of the magnetic field in one-species is strictly weaker than the one in two-species. As a by-product, the global existence of solutions to the nonlinear Cauchy problem is also proved by constructing some similar energy functionals but the time-decay rates of the obtained solution still remain open.
 In this paper we study the large-time behavior of classical solutions to the two-species Vlasov-Maxwell-Boltzmann system in the whole space amssym @math . The existence of global-in-time nearby Maxwellian solutions is known from Strain in 2006. However, the asymptotic behavior of these solutions has been a challenging open problem. Building on our previous work on time decay for the simpler Vlasov-Poisson-Boltzmann system, we prove that these solutions converge to the global Maxwellian with the optimal decay rate of O(t−3 2 + 3 (2r)) in the L (L)-norm for any 2 ≤ r ≤ ∞ if initial perturbation is smooth enough and decays in space velocity fast enough at infinity. Moreover, some explicit rates for the electromagnetic field tending to 0 are also provided. © 2011 Wiley Periodicals, Inc. The Vlasov–Maxwell–Boltzmann system is one of the most fundamental models to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove existence of global in time classical solutions to the Cauchy problem near Maxwellians.