Geodesic
Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov's form
Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 468-480

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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.
Mots-clés : Vlasov equation, magnetohydrodynamics equations
Keywords: Lagrange identity, kinetic equation. 
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     author = {V. V. Vedenyapin and M. A. Negmatov},
     title = {Derivation and classification of {Vlasov-type} and magnetohydrodynamics equations: {Lagrange} identity and {Godunov's} form},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {170},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a10/}
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V. V. Vedenyapin; M. A. Negmatov. Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov's form. Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 468-480. http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a10/