发表机构
Morningside Center of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences (CAS); Department of Mathematics, University of Michigan（中国科学院数学与系统科学研究院; 密歇根大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究二维带两个后退点涡的重力水波系统，通过结合衰减性质、Wu的三次公式及相关论证，证明平表面小局部扰动的整体界，得出系统整体适定性。
AI 中文摘要
我们证明了二维无限深重力水波系统与一对强度相反的点涡耦合时的整体适定性。该涡旋偶极子初始置于自由表面下方深处，其取向使得主导运动远离界面。我们表明这些涡旋几乎线性后退，因此在自由边界上诱导的速度在时间上可积。结合这种衰减、Wu的三次公式以及导数变换和局部化论证，我们得到了平表面小局部扰动的整体界。
英文摘要
We prove global well-posedness for the two-dimensional infinite-depth gravity water wave system coupled to a pair of point vortices of opposite strengths. The vortex dipole is initially placed deep below the free surface and oriented so that its leading motion is away from the interface. We show that the vortices retreat almost linearly, and that the velocity induced on the free boundary is therefore integrable in time. Combining this decay with Wu's cubic formulation, together with a transition-of-derivatives and localization argument, we obtain global bounds for small localized perturbations of the flat surface.
