V. V. Vedenyapin, M. A. Negmatov, “Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov's form”, TMF, 170:3 (2012), 468–480; Theoret. and Math. Phys., 170:3 (2012), 394

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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 170, Number 3, Pages 468–480
DOI: https://doi.org/10.4213/tmf6779 (Mi tmf6779)

This article is cited in 27 scientific papers (total in 27 papers)

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

V. V. Vedenyapin, M. A. Negmatov

Keldysh Institute of Applied Mathematics, RAS, Moscow, Russia

Full-text PDF (439 kB) Citations (27)

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DOI: https://doi.org/10.4213/tmf6779

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.

Keywords: Vlasov equation, magnetohydrodynamics equations, Lagrange identity, kinetic equation.

Received: 23.12.2010
Revised: 29.04.2011

English version:
Theoretical and Mathematical Physics, 2012, Volume 170, Issue 3, Pages 394–405
DOI: https://doi.org/10.1007/s11232-012-0038-1

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. V. Vedenyapin, M. A. Negmatov, “Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov's form”, TMF, 170:3 (2012), 468–480; Theoret. and Math. Phys., 170:3 (2012), 394–405

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https://www.mathnet.ru/eng/tmf/v170/i3/p468

This publication is cited in the following 27 articles:

V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems”, Theoret. and Math. Phys., 218:2 (2024), 222–240
V. V. Vedenyapin, V. M. Aushev, A. O. Gladkov, Yu. A. Izmailova, A. A. Rebrova, “Matematicheskaya teoriya uskorennogo rasshireniya Vselennoi na osnove printsipa naimenshego deistviya i modeli Fridmana i Milna-Makkri”, Preprinty IPM im. M. V. Keldysha, 2024, 003, 28 pp.
V. V. Vedenyapin, A. A. Bay, “Least action principle for gravity and electrodynamics, the Lambda-term and the analog of Milne–McCrea solution for Lorentzian metric”, Eur. Phys. J. Plus, 139:2 (2024)
V.V. Vedenyapin, A.A. Bay, V.I. Parenkina, A.G. Petrov, “Minimal Action Principle for Gravity and Electrodynamics, Einstein Lambda, and Lagrange Points”, Markov Processes And Related Fields, 2024, no. 2023 №4(29), 515
V. V. Vedenyapin, “On Derivation of Vlasov–Maxwell–Einstein Equations from the Principle of Least Action, the Hamilton–Jacobi Method, and the Milne–McCrea Model”, Dokl. Math., 2024
V. V. Vedenyapin, “On derivation of Vlasov–Maxwell–Einstein equations from the principle of least action, Hamilton–Jacobi method and Milne–McCree Model”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 515:1 (2024), 60
V. V. Vedenyapin, D. A. Kogtenev, “O vyvode i svoistvakh uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2023, 020, 18 pp.
V. V. Vedenyapin, A. A. Bay, A. G. Petrov, “On derivation of equations of gravitation from the principle of least action, relativistic Milne-Mccree solutions and Lagrange points”, Dokl. Math., 108:3 (2023), 481–485
V. V. Vedenyapin, “On derivation of equations of electrodynamics and gravitation from the principle of least action, the Hamilton–Jacobi method, and cosmological solutions”, Dokl. Math., 105:3 (2022), 178–182
V. V. Vedenyapin, V. I. Parenkina, A. G. Petrov, Chzhan Khaochen, “Uravnenie Vlasova-Einshteina i tochki Lagranzha”, Preprinty IPM im. M. V. Keldysha, 2022, 023, 23 pp.
V. V. Vedenyapin, V. I. Parenkina, S. R. Svirshchevskii, “Derivation of the equations of electrodynamics and gravity from the principle of least action”, Comput. Math. Math. Phys., 62:6 (2022), 983–995
Vedenyapin V.V., Fimin N.N., Chechetkin V.M., “Properties of the Vlasov-Maxwell-Einstein Equations and Their Application to the Problems of General Relativity”, Gravit. Cosmol., 26:2 (2020), 173–183
Vedenyapin V., Fimin N., Chechetkin V., “The System of Vlasov-Maxwell-Einstein-Type Equations and Its Nonrelativistic and Weak Relativistic Limits”, Int. J. Mod. Phys. D, 29:1 (2020), 2050006
Vedenyapin V.V., Voronina M.Yu., Russkov A.A., “Derivation of the Equations of Electrodynamics and Gravitation From the Principle of Least Action”, Dokl. Phys., 65:12 (2020), 413–417
S. Z. Adzhiev, Ya. G. Batishcheva, V. V. Vedenyapin, Yu. A. Volkov, V. V. Kazantseva, I. V. Melikhov, M. A. Negmatov, Yu. N. Orlov, N. N. Fimin, V. M. Chechetkin, “S.K. Godunov and kinetic theory at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences”, Comput. Math. Math. Phys., 60:4 (2020), 610–614
V. V. Vedenyapin, S. Z. Adzhiev, Ya. G. Batischeva, Yu. A. Volkov, V. V. Kazantseva, I. V. Melikhov, Yu. N. Orlov, M. A. Negmatov, N. N. Fimin, V. M. Chechetkin, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020, 381
V. V. Vedenyapin, I. S. Pershin, “Vlasov–Maxwell–Einstein equation and Einstein lambda”, Preprinty IPM im. M. V. Keldysha, 2019, 039, 17 pp.
V. V. Vedenyapin, N. S. Smirnova, “Uravneniya Eilera i Nave–Stoksa kak sledstviya uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2019, 041, 20 pp.
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Equation of Vlasov–Maxwell–Einstein type and transition to a weakly relativistic approximation”, Comput. Math. Math. Phys., 59:11 (2019), 1816–1831
Victor V. Vedenyapin, Nikolai N. Fimin, Valeriy M. Chechetkin, “DERIVATION OF VLASOV-MAXWELL-EINSTEIN EQUATION AND ITS CONNECTION WITH COSMOLOGICAL LAMBDA-TERM”, Bulletin of the MSRU (Physics and Mathematics), 2019, no. 2, 24

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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