Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data

@misc{wang2026long,
  title = {{Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data}},
  author = {Yubo Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.01778},
  eprint = {2606.01778},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.01778},
}

TY  - UNPB
TI  - Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data
AU  - Yubo Wang
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2606.01778
UR  - https://arxiv.org/abs/2606.01778
AB  - This paper investigates the long time well-posedness of the Benjamin-Ono (BO) equation with quasi-periodic initial data in analytic space. We demonstrate that the Lax operator of the BO equation exhibits a trivial spectrum, and elucidate the fundamental mathematical obstacles to establishing global well-posedness. Furthermore, by employing Tao's gauge transformation in conjunction with the Birkhoff Normal Form method, we extend the lifespan of the solutions to O(ε^−3).
ER  -