### Abstract

We prove stability for arbitrarily long times of the zero solution for the so-called β-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the two-dimensional incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of nonlinear dispersive equations. The dispersive operator, L_{1}:(Formula presented.), exhibits good decay, but has numerous unfavorable properties, chief among which are its anisotropy and its behavior at small frequencies.

Original language | English (US) |
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Pages (from-to) | 1425-1471 |

Number of pages | 47 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 70 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Elgindi, T. M., & Widmayer, K. (2017). Long Time Stability for Solutions of a β-Plane Equation.

*Communications on Pure and Applied Mathematics*,*70*(8), 1425-1471. https://doi.org/10.1002/cpa.21676