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 $O(\epsilon^{-3})$.
From: Yubo Wang [view email]
[v1]
Mon, 1 Jun 2026 06:59:21 UTC (19 KB)
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