Stability of Lamb dipoles
Analysis of PDEs
2019-11-06 v1
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.
Cite
@article{arxiv.1911.01795,
title = {Stability of Lamb dipoles},
author = {Ken Abe and Kyudong Choi},
journal= {arXiv preprint arXiv:1911.01795},
year = {2019}
}
Comments
41 pages