### Abstract

We address the problem of analyticity of smooth solutions u of the incompressible Euler equations. If the initial datum is real-analytic, the solution remains real-analytic as long as ∫^{t}_{0} ∥∇ u(-,s) ∥_{L∞} ds < ∞.Using a Gevrey-class approach we obtain lower bounds on the radius of space analyticity which depend algebraically on exp ∫^{t}_{0} ∥∇u(·,s)∥_{L∞}ds.In particular, we answer in the positive a question posed by Levermore and Oliver.

Original language | English (US) |
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Pages (from-to) | 669-677 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2009 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Kukavica, I., & Vicol, V. (2009). On the radius of analyticity of solutions to the three-dimensional Euler equations.

*Proceedings of the American Mathematical Society*,*137*(2), 669-677. https://doi.org/10.1090/S0002-9939-08-09693-7