1. Stability of Lamb Dipoles
- Author
-
Ken Abe and Kyudong Choi
- Subjects
Mathematics - Analysis of PDEs ,Mathematics (miscellaneous) ,orbital stability ,Mechanical Engineering ,FOS: Mathematics ,Lamb dipole ,Physics::Atomic Physics ,vortex pairs ,Euler equations ,Analysis ,Analysis of PDEs (math.AP) - 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., Comment: 41 pages
- Published
- 2022