We prove the discontinuity for the weak L2(T)-topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in Hs(T) as soon as s < 0 and thus completes exactly the well-posedness result obtained in Molinet (2008) . © 2009 Elsevier Inc. All rights reserved.
Molinet, L. (2009). Sharp ill-posedness result for the periodic Benjamin-Ono equation. Journal of Functional Analysis, 257(11), 3488–3516. https://doi.org/10.1016/j.jfa.2009.08.018