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

详细信息    查看全文

• 作者：V. V. Vedenyapin (1) vicveden@yahoo.com
  M. A. Negmatov (1) maliknegmatov@gmail.com
• 关键词：Vlasov equation – magnetohydrodynamics equations – Lagrange identity – kinetic equation
• 刊名：Theoretical and Mathematical Physics
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：170
• 期：3
• 页码：394-405
• 全文大小：363.2 KB
• 参考文献：1. A. A. Vlasov, Zh. Eksp. Teor. Fiz., 8, No. 3, 291–318 (1938).
  2. A. A. Vlasov, Nonlocal Statistical Mechanics [in Russian], Nauka, Moscow (1978).
  3. N. N. Bogoliubov, Problems of Dynamical Theory in Statistical Physics [in Russian], Gostekhizdat, Moscow (1946).
  4. V. P. Maslov and P. P. Mosolov, Math. USSR-Izv., 13, 349–386 (1979).
  5. L. D. Landau and E. M. Lifshitz, Theoretical Physics [in Russian], Vol. 2, Field Theory, Nauka, Moscow (1988); English transl. prev. ed.: The Classical Theory of Fields, Pergamon, Oxford (1975).
  6. V. V. Vedenyapin, Kinetic Equations of Boltzmann and Vlasov [in Russian], Fizmatlit, Moscow (2001).
  7. M. B. Gavrikov and V. V. Savel’ev, Fluid Dyn., 45, 325–341 (2010). <Occurrence Type="Bibcode"><Handle>2010FlDy...45..325G</Handle></Occurrence>
  8. V. V. Kozlov, Russ. Math. Surveys, 63, 691–726 (2008). <Occurrence Type="Bibcode"><Handle>2008RuMaS..63..691K</Handle></Occurrence>
  9. W. Braun and K. Hepp, Commun. Math. Phys., 56, 101–113 (1977). <Occurrence Type="Bibcode"><Handle>1977CMaPh..56..101B</Handle></Occurrence>
  10. W. Pauli, Theory of Relativity, Pergamon, London (1958).
  11. E. M. Lifshitz and L. P. Pitaevskii, Theoretical Physics [in Russian], Vol. 10, Physical Kinetics, Nauka, Moscow (1979); English transl., Pergamon, Oxford (1981).
  12. K. V. Brushlinskii, Mathematical and Computational Problems of Magnetic Gas Dynamics [in Russian], Binom, Moscow (2009).
  13. L. D. Landau and E. M. Lifshitz, Theoretical Physics [in Russian], Vol. 8, Electrodynamics of Continuous Media, Nauka, Moscow (1982); English transl. (2nd ed., rev. and enl. by E. M. Lifshitz and L. P. Pitaevskii), Pergamon, Oxford (1984).
  14. A. G. Kulikovskii and G. A. Lyubimov, Magnetohydrodynamics [in Russian], Logos, Moscow (2005).
  15. S. I. Braginskii, “Manifestations of transport in plasma [in Russian],” in: Questions of Plasma Theory (M. A. Leontovich, ed.), Vol. 1, Gostekhizdat, Moscow (1963), p. 183–272; English transl.: “Transport processes in a plasma,” in: Reviews of Plasma Physics, Vol. 1, Consultants Bureau, New York (1965), pp. 205–311.
  16. J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases, North-Holland, Amsterdam (1972).
• 作者单位：1. Keldysh Institute of Applied Mathematics, RAS, Moscow, Russia
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Applications of Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9333

文摘

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.