发表机构
Osaka Metropolitan University; Korea Institute for Advanced Study; Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Xiamen University（大阪公立大学; 韩国高等研究院; 中国科学院数学与系统科学研究院; 厦门大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文统一描述了二维欧拉方程中行波涡偶极子的变分族，揭示了从兰姆偶极子到大冲量径向偶极子的尖锐过渡，证明了临界值、平移唯一性及轨道稳定性。
AI 中文摘要
我们为二维不可压缩欧拉方程的一族稳定的行波涡偶极子提供了统一描述，该族将经典兰姆偶极子与大冲量区域中的渐近径向偶极子联系起来。我们证明，该族经历了一个从质量约束不活跃的兰姆偶极子到质量约束变得活跃的非显式行波的尖锐过渡，并精确确定了临界值。我们进一步证明，在兰姆偶极子附近和大冲量区域中，变分解在平移意义下是唯一的。因此，相应的单个行波是轨道稳定的。我们的结果为单个行波涡偶极子变分族中的这两个不同渐近区域提供了统一图景。
英文摘要
We provide a unified description of a stable variational family of traveling vortex dipoles for the two-dimensional incompressible Euler equations, connecting the classical Lamb dipole to asymptotically radial dipoles in the large-impulse regime. We show that this family undergoes a sharp transition from the Lamb dipole, where the mass constraint is inactive, to non-explicit traveling waves for which the mass constraint becomes active, and determine the critical value exactly. We further prove that the variational solutions are unique up to translation both near the Lamb dipole and in the large-impulse regime. As a consequence, the corresponding individual traveling waves are orbitally stable. Our results provide a unified picture of these two distinct asymptotic regimes within a single variational family of traveling vortex dipoles.
Comments44 pages, 4 figures
