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Derivation of Ohm’s law from the kinetic equations. (English) Zbl 1257.35141
Summary: 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.
MSC:
35Q20Boltzmann equations
35Q61Maxwell equations
35Q83Vlasov-like equations
76W05Magnetohydrodynamics and electrohydrodynamics