标题： 多个兰姆偶极子的稳定性 显示英文标题

标题： Stability for multiple Lamb dipoles

摘要： 在半平面的非负涡度类中，我们在初始假设下建立了有限个兰姆偶极子的李雅普诺夫稳定性，这些假设包括偶极子之间足够分离，且较快的偶极子位于较慢的偶极子右侧。 我们的方法结合了接近兰姆偶极子的精确能量估计与拉格朗日自举方案，使我们能够量化解的不同部分之间环量、涡量、动量和能量的交换。 证明的策略具有鲁棒性，我们提出了该结果的几个潜在扩展。 显示英文摘要

摘要： In the class of nonnegative vorticities on the half-plane, we establish the Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that the dipoles are sufficiently separated and that the faster dipoles are positioned to the right of the slower ones. Our approach combines sharp energy estimates near the Lamb dipoles with a Lagrangian bootstrapping scheme, enabling us to quantify the exchanges of circulation, enstrophy, impulse, and energy between various parts of the solution. The strategy of the proof is robust, and we present several potential extensions of the result.