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The goal of this article is to give a formal derivation of Ohm's law of magnetohydrodynamics (MHD) starting from the Vlasov--Maxwell--Boltzmann system. The derivation is based on various physical scalings and the moment methods when the Knudsen number goes to zero. We also give a derivation of the so-called Hall effect as well as other limit models such as the Navier--Stokes--Maxwell system. Our results include both the compressible and incompressible MHD models.
Jang et al. (Sun,) studied this question.
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