## Abstract

The steady-state kinematic dynamo problem in a homogeneous 3-dimensional core is studied. The existence of a class of smooth solenoidal dynamos, satisfying a no-slip condition on the core boundary, is proved using perturbation theory. The dynamos are of the form q = q^{(1)} + q ^{(2)} + q^{(3)}, where q^{(1)} is spatially periodic on a sufficiently small scale of length, q^{(2)} is zero except near the core boundary, and q^{(3)} is an arbitrary sufficiently small motion. The term q^{(1)} is also a spatially periodic dynamo in an appropriate sense for an infinite core. The last property allows a simple characterization of the bounded dynamos in terms of the admissible q^{(1)}.

Original language | English |
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Pages (from-to) | 3063-3076 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 11 |

Issue number | 10 |

DOIs | |

State | Published - 1970 |

Externally published | Yes |