## 抄録

A novel linear stability criterion is established for the equilibria of general three-dimen- sional (3D) rotating ows of an ideal gas satisfying Boyle–Charles' law by a newly refined energy-Casimir convexity (ECC) method that can exploit a larger class of Casimir in- variants. As the conventional ECC method cannot be applied directly to stratified shear ows, in our new approach, rather than checking the local convexity of a Lyapunov func- tional L ≡ E + C_{E} defined as a sum of the total energy and a certain Casimir, we seek the condition for nonexistence of unstable manifolds: orbits (physically realisable ow in phase space) on the leaves of invariants including L as well as other Casimirs connecting a given equilibrium point O and other points in the neighbourhood of it. We argue that the separatrices of the second variation of L (δ^{2}L = 0) generally consist of such unstable manifolds as well as pseudo unstable ones for which either the total energy or Casimirs actually serve as a barrier for escaping orbits. The significance of the new method lies in the fact that it eliminates the latter so as to derive a condition for O being an isolated equilibrium point in terms of orbital connections.

本文言語 | 英語 |
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ページ（範囲） | 605-633 |

ページ数 | 29 |

ジャーナル | Publications of the Research Institute for Mathematical Sciences |

巻 | 51 |

号 | 4 |

DOI | |

出版ステータス | 出版済み - 1 1 2015 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)