Instability of the Periodic Nonlinear Schr¨odinger Equation

@inproceedings{Christ2003InstabilityOT,
title={Instability of the Periodic Nonlinear Schr¨odinger Equation},
author={Michael Christ and J. Colliander and Terence Tao},
year={2003}
}

We study the periodic non-linear Schrodinger equation −iu t +u xx = ±|u| p−1 u for initial data which are assumed to be small in some negative order Sobolev space H s (T) (s < 0), but which may have large L 2 mass. In [6], [7] these equations were shown to be ill-posed in H s (T), in the sense that the solution map was not uniformly continuous from H s (T) to itself even for short times and small norms. Here we show that these equations are even more unstable, in different ways for different p… CONTINUE READING