Gases and Fluids

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

Yu. G. Gubarev<sup>ab

a</sup> Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

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.

Received: 01.02.2011
Accepted: 23.05.2011

 English version: Technical Physics, 2012, 57:1, 12–16

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