Skip to main content
SpringerLink
Log in

Spectral properties of a linearized model of magnetohydrodynamics

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

Abstract

One considers the frequency spectrum of the linear oscillations of a perfectly conducting nonviscous plasma with a nonzero pressure. It is shown that the essential spectrum for each of the harmonic modes is not empty and can consist of at most two finite intervals (or points). The discrete spectrum contains an infinite number of eigenvalues, diverging to +∞. One has found the first term of the asymptotics of this sequence. One shows the absence of the accumulation of the eigenvalues towards the endpoints of one of the intervals of the essential spectrum and also the absence of the eigenvalues to the left of the essential spectrum.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. L. Krylov, A. E. Lifshits, and E. N. Fedorov, “On resonance properties of magnetospheres,” Fiz. Zemli, No. 6, 49–58 (1981).

    Google Scholar 

  2. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  3. O. A. Ladyzhenskaya, The Mathematical Problems of the Dynamics of a Viscous Incompressible Fluid [in Russian], Nauka, Moscow (1961).

    Google Scholar 

  4. M. Sh. Birman and M. Z. Solomyak, “The spectral asymptotics of nonsmooth elliptic operators. I,” Trudy Moskov. Mat. Obshch.,27, 3–52 (1972).

    Google Scholar 

  5. M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in a Hilbert Space [in Russian], Leningrad. Univ. (1980).

  6. M. Sh. Birman, “On the spectrum of singular boundary problems,” Mat. Sb.,55 (97), 125–174 (1961).

    Google Scholar 

  7. S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of People's Republic of Bulgaria, Bulgaria

    G. D. Raikov

Authors
  1. G. D. Raikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 195–207, 1986.

In conclusion the author expresses his deep gratitude to his scientific advisor M. Sh. Birman for his help and numerous discussions and to A. E. Lifshits for consultations and for his interest in this paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Raikov, G.D. Spectral properties of a linearized model of magnetohydrodynamics. J Math Sci 45, 1261–1271 (1989). https://doi.org/10.1007/BF01096158

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01096158

Keywords

Search

Navigation