We prove the ill-posedness in H s (T), s < 0, of the periodic cubic Schrödinger equation in the sense that the flow-map is not continuous from H s (T) into itself for any fixed t = 0. This result is slightly stronger than the one in  where the discontinuity of the solution map is established. Moreover our proof is different and clarifies the ill-posedness phenomena. Our approach relies on a new result on the behavior of the associated flow-map with respect to the weak topology of L²(T)
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.