Sharp ill-posedness result for the periodic Benjamin-Ono equation

Luc Molinet (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We prove the discontinuity for the weak $ L^2(\T) $-topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in $ H^s(\T) $ as soon as $ s<0 $ and thus completes exactly the well-posedness result obtained by the author.

Mots clés: Benjamin-Ono equation; Continuity with respect to initial data.; Continuity with respect to initial data

Domaines: Equations aux dérivées partielles [math.AP]

Luc Molinet. Sharp ill-posedness result for the periodic Benjamin-Ono equation. Journal of Functional Analysis, 2009, 257, pp.3488-3516. ⟨hal-00336559v1⟩