### Abstract

The authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3-D Euler equations. In other words, if a solution of the Euler equations is initially smooth and loses its regularity at some later time, then the maximum vorticity necessarily grows without bound as the critical time approaches; equivalently, if the vorticity remains bounded, a smooth solution persists.

Original language | English (US) |
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Pages (from-to) | 61-66 |

Number of pages | 6 |

Journal | Communications In Mathematical Physics |

Volume | 94 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1984 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Beale, J. T., Kato, T., & Majda, A. (1984). Remarks on the breakdown of smooth solutions for the 3-D Euler equations.

*Communications In Mathematical Physics*,*94*(1), 61-66. https://doi.org/10.1007/BF01212349