Stability of Lamb Dipoles
Stability of Lamb Dipoles
复制标题
兰姆偶极子的稳定性
DOI：
10.1007/s00205-022-01782-4
复制
发表时间：
2022
影响因子：
2.5
通讯作者：
Choi Kyudong
中科院分区：
文献类型：
--
作者：
Abe Ken;Choi Kyudong
兰姆偶极子是Chaobergin（Trudy Otd Fiz Nauk英佩尔Mosk Obshch Lyub Estest 11：11-14，1903）和Lamb（Hydrodynamics，1906）提出的二维欧拉方程的行波解。在世纪早期。我们证明了这个解决方案的基础上的涡度方法Arnold的轨道稳定性。我们的方法是一个惩罚的能量与多个约束，推导出的存在性和轨道稳定性的行波家庭的最小化。作为一个典型的例子，Lamb偶极子的轨道稳定性的推导通过表征一组极小作为一个轨道的偶极子在变分设置的唯一性定理。
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.