Global theory for quintic and higher regularised Benjamin–Ono equations

Establish global well-posedness for the quintic and higher-power regularised Benjamin–Ono equations in the low-regularity regimes not covered by the cubic theory.

Background

The paper proves endpoint global well-posedness in H{1/2}(T) for the cubic regularised Benjamin–Ono equation. It explains that the compactness and uniqueness method used for the cubic equation does not extend to higher powers. Consequently, the corresponding theory for the quintic and higher nonlinearities remains unresolved.

References

The theory for the quintic and higher powers of the regularised BO equation remains unknown as the compactness method used in this paper is insufficient (see Remark \ref{Local:endpoint:failure_remark}).

— Well-posedness for the generalised fractional BBM equation  (2610.03288 - Barratt, 2 Oct 2026) in Section 1, subsection “Endpoint well-posedness”