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arXiv · 2605.27869

Global Well-Posedness for the Benjamin-Ono Equation with Small Periodic Initial Data in Analytic Spaces

Yubo Wang
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Abstract

We establish global well-posedness of the Benjamin--Ono equation for sufficiently small, zero-mean periodic initial data in the analytic Sobolev space $H^{\rho,1}_0$. The proof combines regularized commuting flows with an exponential spectral energy. A local uniform convexity property of this energy upgrades weak endpoint compactness to strong continuity, yielding a global flow in $C(\mathbb{R};H^{\rho,1}_0)$ and continuous dependence in the same analytic topology, with no dynamic loss of the prescribed analytic width.

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Yubo Wang. 2026-05-27. Global Well-Posedness for the Benjamin-Ono Equation with Small Periodic Initial Data in Analytic Spaces. https://arxiv.org/abs/2605.27869

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