### Abstract

In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.

Original language | English |
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Pages (from-to) | 445-463 |

Number of pages | 19 |

Journal | Communications in Mathematical Physics |

Volume | 324 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 2013 |

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## Cite this

Burton, G., Nussenzveig Lopes, H., & Lopes Filho, M. C. (2013). Nonlinear stability of steady vortex pairs.

*Communications in Mathematical Physics*,*324*(2), 445-463. https://doi.org/10.1007/s00220-013-1806-y