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- Choi, Kyudong
- Fluids Analysis Lab.
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Stability of Lamb dipoles
- Author(s)
- Abe, Ken, Choi, Kyudong
- Issued Date
- 2022-06
- Citation
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.244, no.3, pp.877 - 917
- Abstract
- The Lamb dipole is a traveling wave solution to the two-dimensional Euler equations introduced by Chaplygin (Trudy Otd Fiz Nauk Imper Mosk Obshch Lyub Estest 11:11-14, 1903) and Lamb (Hydrodynamics, 1906.) at the early 20th century. We prove the orbital stability of this solution based on a vorticity method initiated by 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, the 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.
- Publisher
- SPRINGER
- ISSN
- 0003-9527
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