### Abstract

Ruelle has found upper bounds to the magnitude and to the number of non-negative characteristic exponents for the Navier-Stokes flow of an incompressible fluid in a domain Θ. The latter is particularly important because it yields an upper bound to the Hausdorff dimension of attracting sets. However, Ruelle's bound on the number has three deficiences: (i) it relies on some unproved conjectures about certain constants; (ii) it is valid only in dimensions ≧ 3 and not 2; (iii) it is valid only in the limit Θ → ∞. In this paper these deficiences are remedied and, in addition, the final constants in the inequality are improved.

Original language | English (US) |
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Pages (from-to) | 473-480 |

Number of pages | 8 |

Journal | Communications In Mathematical Physics |

Volume | 92 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1984 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lieb, E. (1984). On characteristic exponents in turbulence.

*Communications In Mathematical Physics*,*92*(4), 473-480. https://doi.org/10.1007/BF01215277