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Global regularity for 2D gravity water waves with two retreating point vortices

  • Lei Su
  • Qingtang Su
  • Siwei Wang
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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.

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Cite

BibTeXRIS
BibTeX
@misc{su2026global,
  title = {{Global regularity for 2D gravity water waves with two retreating point vortices}},
  author = {Lei Su and Qingtang Su and Siwei Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01250},
  eprint = {2609.01250},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01250},
}
RIS
TY  - UNPB
TI  - Global regularity for 2D gravity water waves with two retreating point vortices
AU  - Lei Su
AU  - Qingtang Su
AU  - Siwei Wang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01250
UR  - https://arxiv.org/abs/2609.01250
AB  - 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.
ER  -