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The motion of a fully ionized plasma of electrons and ions is generallygoverned by the Vlasov-Maxwell-Landau system. We prove the global existence ofsolutions near Maxwellians to the Cauchy problem of the system for thelong-range collision kernel of soft potentials, particularly including theclassical Coulomb collision, provided that initial data is smooth enough anddecays in velocity variable fast enough. As a byproduct, the convergence ratesof solutions are also obtained. The proof is based on the energy method throughdesigning a new temporal energy norm to capture different features of thiscomplex system such as dispersion of the macro component in $\mathbb{R}^3$,singularity of the long-range collisions and regularity-loss of theelectromagnetic field.

Global smooth dynamics of a fully ionized plasma with long-range collisions