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- Title
Stability of Lamb Dipoles.
- Authors
Abe, Ken; Choi, Kyudong
- 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.
- Subjects
LAMBS; FAMILY stability; FAMILY travel; TWENTIETH century; VORTEX motion; EULER equations
- Publication
Archive for Rational Mechanics & Analysis, 2022, Vol 244, Issue 3, p877
- ISSN
0003-9527
- Publication type
Article
- DOI
10.1007/s00205-022-01782-4