Stability of Lamb dipoles

Ken Abe; Kyudong Choi

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arXiv · 1911.01795

Stability of Lamb dipoles

Ken Abe·Kyudong Choi

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Abstract

The Lamb dipole is a traveling wave solution to the two-dimensional Euler equations introduced by S. A. Chaplygin (1903) and H. Lamb (1906) at the early 20th century. We prove orbital stability of this solution based on a vorticity method initiated by V. I. Arnold. Our method is a minimization of a penalized energy with multiple constraints that deduces existence and orbital stability for a family of traveling waves. As a typical case, orbital stability of the Lamb dipole is deduced by characterizing a set of minimizers as an orbit of the dipole by a uniqueness theorem in the variational setting.

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Ken Abe, Kyudong Choi. 2019-11-05. Stability of Lamb dipoles. https://arxiv.org/abs/1911.01795

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