Year: 2026
Type: preprint
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 $O(ε^{-3})$.
Source: arXiv (Cornell University)
Author: Wang, Yubo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163255146