Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation

The energy method was used to investigate the stability of steady magnetohydrodynamic flows in an inviscid incompressible fluid. It was found that if a given steady magnetohydrodynamic flow is stable by the energy method, then certain infinite-dimensional families of steady flows obtained from the given flow by these transformations were also stable. Sufficient conditioons for linear stability were obtained from these results. Thus, it was shown that certain classes of steady magnetohydrodynamic flows, in which both the magnetic field and the velocity depend on all the three spatial coordinates, are stable.