### Abstract

The Cauchy problem of the Euler equations in the whole space is considered with non-decaying initial velocity in the frame work of B_{∞,1}^{1}. It is proved that if the initial velocity is real analytic then the solution is also real analytic in spatial variables. Furthermore, a new estimate for the size of the radius of convergence of Taylor's expansion is established. The key of the proof is to derive the suitable estimates for the higher order derivatives of the bilinear terms. It is also shown the propagation of the almost periodicity in spatial variables.

Original language | English |
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Pages (from-to) | 2148-2162 |

Number of pages | 15 |

Journal | Journal of Functional Analysis |

Volume | 260 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2011 Apr 1 |

### Keywords

- Almost periodicity
- Analyticity
- Non-decaying initial velocity
- The Euler equations

### ASJC Scopus subject areas

- Analysis

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## Cite this

Sawada, O., & Takada, R. (2011). On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity.

*Journal of Functional Analysis*,*260*(7), 2148-2162. https://doi.org/10.1016/j.jfa.2010.12.011