In this paper we consider Schr{ \"o}dinger equations with nonlinearities of odd order 2$\sigma$ + 1 on T^d. We prove that for $\sigma$d$\ge$2, they are strongly illposed in the Sobolev space H^s for any s \textless{ } 0, exhibiting norm-inflation with infinite loss of regularity. In the case of the one-dimensional cubic nonlinear Schr{ \"o}dinger equation and its renormalized version we prove such a result for H^s with s \textless{ } --2/3.
Categories: math.AP