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TMF, 2012, Volume 170, Number 3, Pages 468–480 (Mi tmf6779)  

This article is cited in 9 scientific papers (total in 9 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

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

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

Full text: PDF file (439 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 170:3, 394–405

Bibliographic databases:

Received: 23.12.2010
Revised: 29.04.2011

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Vedenyapin V.V., Fimin N.N., “The Liouville equation, the hydrodynamic substitution, and the Hamilton–Jacobi equation”, Dokl. Math., 86:2 (2012), 697–699  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. Vedenyapin V.V., Negmatov M.A., “On the Topology of Steady-State Solutions of Hydrodynamic and Vortex Consequences of the Vlasov Equation and the Hamilton–Jacobi Method”, Dokl. Math., 87:2 (2013), 240–244  crossref  mathscinet  zmath  isi  elib  scopus
    3. S. L. Ginzburg, V. F. Dyachenko, V. S. Imshennik, “3D-model of interaction between powerful laser radiation with plasma supercritical density and generation of high-energy protons”, Math. Models Comput. Simul., 7:3 (2015), 203–213  mathnet  crossref
    4. V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. Math., 81:3 (2017), 505–541  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. V. V. Vedenyapin, A. A. Andreeva, V. V. Vorobyeva, “Euler and Navier–Stokes equations as self-consistent fields”, Dokl. Math., 97:3 (2018), 283–285  mathnet  crossref  crossref  zmath  isi  elib  scopus
    6. V. V. Vedenyapin, “Uravnenie Vlasova–Maksvella–Einshteina”, Preprinty IPM im. M. V. Keldysha, 2018, 188, 20 pp.  mathnet  crossref  elib
    7. V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Ob uravnenii Vlasova–Maksvella–Einshteina i ego nerelyativistskikh i slaborelyativistskikh analogakh”, Preprinty IPM im. M. V. Keldysha, 2018, 265, 30 pp.  mathnet  crossref  elib
    8. V. V. Vedenyapin, I. S. Pershin, “Vlasov–Maxwell–Einstein equation and Einstein lambda”, Preprinty IPM im. M. V. Keldysha, 2019, 039, 17 pp.  mathnet  crossref
    9. 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.  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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