### 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) |
---|---|

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 1 2009 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*137*(2), 669-677. https://doi.org/10.1090/S0002-9939-08-09693-7

**On the radius of analyticity of solutions to the three-dimensional Euler equations.** / Kukavica, Igor; Vicol, Vlad.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 137, no. 2, pp. 669-677. https://doi.org/10.1090/S0002-9939-08-09693-7

}

TY - JOUR

T1 - On the radius of analyticity of solutions to the three-dimensional Euler equations

AU - Kukavica, Igor

AU - Vicol, Vlad

PY - 2009/2/1

Y1 - 2009/2/1

N2 - 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 ∫t0 ∥∇ u(-,s) ∥L∞ ds < ∞.Using a Gevrey-class approach we obtain lower bounds on the radius of space analyticity which depend algebraically on exp ∫t0 ∥∇u(·,s)∥L∞ds.In particular, we answer in the positive a question posed by Levermore and Oliver.

AB - 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 ∫t0 ∥∇ u(-,s) ∥L∞ ds < ∞.Using a Gevrey-class approach we obtain lower bounds on the radius of space analyticity which depend algebraically on exp ∫t0 ∥∇u(·,s)∥L∞ds.In particular, we answer in the positive a question posed by Levermore and Oliver.

UR - http://www.scopus.com/inward/record.url?scp=70350612106&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350612106&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09693-7

DO - 10.1090/S0002-9939-08-09693-7

M3 - Article

AN - SCOPUS:70350612106

VL - 137

SP - 669

EP - 677

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -