Almost sure well-posedness of the cubic nonlinear Schr\

@inproceedings{Colliander2009AlmostSW,
  title={Almost sure well-posedness of the cubic nonlinear Schr\},
  author={James E. Colliander and Tadahiro Oh},
  year={2009}
}
We consider the Cauchy problem for the one-dimensional periodic cubic non- linear Schrodinger equation (NLS) with initial data below L 2 . In particular, we exhibit nonlinear smoothing when the initial data are randomized. Then, we prove local well- posedness of NLS almost surely for the initial data in the support of the canonical Gaussian measures on H s (T) for each s > − 1 , and global well-posedness for each s > − 1 12 . 
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