### Abstract

We consider the incompressible Euler equations on R^{d} or T^{d}, where d∈{2,3}. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a fixed Gevrey-class radius). (b) In Lagrangian coordinates the equations are locally well-posed in highly anisotropic spaces, e.g. Gevrey-class regularity in the label a_{1} and Sobolev regularity in the labels a_{2},…,a_{d}. (c) In Eulerian coordinates both results (a) and (b) above are false.

Original language | English (US) |
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Pages (from-to) | 1569-1588 |

Number of pages | 20 |

Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |

Volume | 33 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1 2016 |

### Keywords

- Analyticity
- Euler equations
- Gevrey class
- Lagrangian and Eulerian coordinates

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Applied Mathematics

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## Cite this

Constantin, P., Kukavica, I., & Vicol, V. (2016). Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations.

*Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire*,*33*(6), 1569-1588. https://doi.org/10.1016/j.anihpc.2015.07.002