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On the stability of one class of steady axisymmetric flows of an ideal liquid in a magnetic field

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Abstract

The stability of a particular class of steady axisymmetric magnetohydrodynamic flows of a nonviscous incompressible liquid with a uniform density and an infinite conductivity against perturbations of the same symmetry is studied. It is proved by using the direct Lyapunov method that the flows are absolutely stable against imposed perturbations both in a linear approximation and in an exact nonlinear statement. A priori upper estimates indicate that the integrals of the sum of the squares of perturbations of the velocity field’s radial and angular components over the cross section of the flow are limited in time by their initial data.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 15, Novosibirsk, 630090, Russia

    Yu. G. Gubarev

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    Yu. G. Gubarev

Authors
  1. Yu. G. Gubarev
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Correspondence to Yu. G. Gubarev.

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Original Russian Text © Yu.G. Gubarev, 2012, published in Zhurnal Tekhnicheskoi Fiziki, 2012, Vol. 82, No. 1, pp. 14–18.

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Gubarev, Y.G. On the stability of one class of steady axisymmetric flows of an ideal liquid in a magnetic field. Tech. Phys. 57, 12–16 (2012). https://doi.org/10.1134/S1063784212010112

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  • DOI: https://doi.org/10.1134/S1063784212010112

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