Skip to main content
SpringerLink
Log in

Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We describe asymptotic solutions of the Cauchy problem for a linearized system of magnetohydrodynamics with initial conditions localized in a small neighborhood of a curve or a two-dimensional surface. We investigate how a change of the multiplicity of characteristics affects such solutions and prove a uniform estimate of the residual.

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

References

  1. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluid, Cambridge Univ. Press, Cambridge (1978).

    Google Scholar 

  2. S. Friedlander and M. M. Vishik, “On stability and instability criteria for magnetohydrodynamics,” Chaos, 5, 416–423 (1995).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. V. V. Kucherenko, “Waves in the linearized system of magnetohydrodynamics,” Russ. J. Math. Phys., 17, 272–279 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  4. V. V. Kucherenko and A. Kryvko, “Interaction of Alfven waves in the linearized system of magnetohydrodynamics for an incompressible ideal fluid,” Russ. J. Math. Phys., 20, 56–67 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  5. V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973); English transl.: Operational Methods, Mir, Moscow (1976).

    Google Scholar 

  6. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N. J. (1964).

    MATH  Google Scholar 

  7. A. I. Shafarevich, “The behavior of the magnetic field in a conducting liquid with a rapidly changing velocity field,” Dokl. Math., 57, 464–466 (1998).

    Google Scholar 

  8. A. I. Esina and A. I. Shafarevich, “Delta-type solutions for a system of induction equations with discontinuous velocity field,” Methods Funct. Anal. Topology, 20, 17–33 (2014).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ishlinskii Institute for Mechanical Problems, RAS, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia

    A. I. Allilueva & A. I. Shafarevich

  3. National Research Center “Kurchatov Institute,”, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

  4. Lomonosov Moscow State University, Moscow, Russia

    A. I. Shafarevich

Authors
  1. A. I. Allilueva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Shafarevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Allilueva.

Additional information

This research is supported by a grant from the Russian Science Foundation (Project No. 16-11-10282).

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 1, pp. 191–204, January, 2017.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Allilueva, A.I., Shafarevich, A.I. Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag. Theor Math Phys 190, 164–175 (2017). https://doi.org/10.1134/S0040577917010147

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577917010147

Keywords

Search

Navigation