  A global solvability result of the Cauchy problem of the two-species
Vlasov-Maxwell-Landau system near a given global Maxwellian is established by
employing an approach different than that of [5]. Compared with that of [5],
the minimal regularity index and the smallness assumptions we imposed on the
initial data are weaker. Our analysis does not rely on the decay of the
corresponding linearized system and the Duhamel principle and thus it can be
used to treat the one-species Vlasov-Maxwell-Landau system for the case of
$\gamma>-3$ and the one-species Vlasov-Maxwell-Boltzmann system for the case of
$-1<\gamma\leq 1$ to deduce the global existence results together with the
corresponding temporal decay estimates.
