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arXiv · 2606.01778

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

Yubo Wang
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Abstract

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 $O(\epsilon^{-3})$.

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Yubo Wang. 2026-06-01. Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data. https://arxiv.org/abs/2606.01778

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