%0 Journal Article
%T On ill-posedness for the one-dimensional periodic cubic Schrodinger equation
%A Luc Molinet
%J Mathematics
%D 2008
%I arXiv
%X We prove the ill-posedness in $ H^s(\T) $, $s<0$, of the periodic cubic Schr\"odinger equation in the sense that the flow-map is not continuous from $H^s(\T) $ into itself for any fixed $ t\neq 0 $. This result is slightly stronger than the one obtained by Christ-Colliander-Tao 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 $ L^2(\T) $.
%U http://arxiv.org/abs/0806.4538v2