Abstract
We describe the derivation of the Vlasov-Maxwell equations from the Lagrangian of classical electrodynamics, from which magnetohydrodynamic-type equations are in turn derived. We consider both the relativistic and nonrelativistic cases: with zero temperature as the exact consequence of the Vlasov-Maxwell equations and with nonzero temperature as a zeroth-order approximation of the Maxwell-Chapman-Enskog method. We obtain the Lagrangian identities and their generalizations for these cases and compare them.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 170, No. 3, pp. 468–480, March, 2012.
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Vedenyapin, V.V., Negmatov, M.A. Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov’s form. Theor Math Phys 170, 394–405 (2012). https://doi.org/10.1007/s11232-012-0038-1
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DOI: https://doi.org/10.1007/s11232-012-0038-1