Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Su, Lei, Su, Qingtang, Wang, Siwei
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206196424
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