### Abstract

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.

Original language | English |
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Pages (from-to) | 3586-3594 |

Number of pages | 9 |

Journal | Physics of Plasmas |

Volume | 11 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2004 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

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## Cite this

Ilin, K. I., & Vladimirov, V. A. (2004). Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation.

*Physics of Plasmas*,*11*(7), 3586-3594. https://doi.org/10.1063/1.1759337