SpringerLink
Log in

Differential Invariants of the Magnetohydrodynamics Under an Action of the Motion Group

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

The thermodynamics of a conductive liquid is considered. The latter is described within the framework of contact geometry. The state and constitutive equations of the medium are obtained from the first principles and notion of symmetry under natural assumptions only. These thermodynamic relations are supplemented by the general laws of charge, mass, momentum, and energy conservation to form a complete system of partial differential equations that describe the motion of the media. Differential invariants of this system under the action of rotations and translations are studied. A complete set of such invariants is obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. J. L. Bansal, Magnetofluiddynamics of Viscous Fluids (Jaipur Publ., Jaipur, India, 1994).

    Google Scholar 

  2. L. D. Landau and E. M. Lifschitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Pergamon, Oxford, 1987), Chap. 1, pp. 2–5.

  3. L. D. Landau and E. M. Lifschitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Pergamon, Oxford, 1987), Chap. 8, p. 226.

  4. L. D. Landau and E. M. Lifschitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Pergamon, Oxford, 1987), Chap. 2, p. 45.

  5. L. D. Landau and E. M. Lifschitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Pergamon, Oxford, 1987), Chap. 2, p. 44.

  6. L. D. Landau and E. M. Lifschitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Pergamon, Oxford, 1987), Chap. 4, p. 113.

  7. H. Alfven, ‘‘Existence of electromagnetic-hydrodynamic waves,’’ Nature (London, U.K.) 150 (3805), 405–406 (1942).

    Article  Google Scholar 

  8. A. Duyunova, V. Lychagin, and S. Tychkov, ‘‘Continuum mechanics of media with inner structures,’’ Differ. Geom. Appl. 74, 101703 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  9. C. Procesi, Lie Groups: An Approach Through Invariants and Representations (Springer, New York, 2005).

    MATH  Google Scholar 

Download references

Funding

The author is supported by the Theoretical Physics and Mathematics Advancement Foundation BASIS, grant 19-7-1-13-5.

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997, Moscow, Russia

    E. A. Ryabushev

Authors
  1. E. A. Ryabushev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. A. Ryabushev.

Additional information

(Submitted by V. V. Lychagin)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ryabushev, E.A. Differential Invariants of the Magnetohydrodynamics Under an Action of the Motion Group. Lobachevskii J Math 43, 2802–2807 (2022). https://doi.org/10.1134/S1995080222130388

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080222130388

Keywords:

Search

Navigation