Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov鈥檚 form

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• 作者：V. V. Vedenyapin (1) vicveden@yahoo.com
  M. A. Negmatov (1) maliknegmatov@gmail.com
• 关键词：Vlasov equation &#8211 ; magnetohydrodynamics equations &#8211 ; Lagrange identity &#8211 ; kinetic equation
• 刊名：Theoretical and Mathematical Physics
• 出版时间：March 2012
• 出版年：2012
• 期刊代码：71_00405779
• 类别：law
• 卷：170
• 期：3
• 页码：394-405
• 数据来源：sp

摘要

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.