ALMOST SURE WELL-POSEDNESS OF THE CUBIC NONLINEAR SCHRODINGER EQUATION BELOW L-2(T)

作者：Colliander James^*; Oh Tadahiro

来源：Duke Mathematical Journal, 2012, 161(3): 367-414.

DOI：10.1215/00127094-1507400

We consider the Cauchy problem for the 1-dimensional periodic cubic nonlinear Schrodinger (NLS) equation 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 the NLS equation almost surely for the initial data in the support of the canonical Gaussian measures on H-s(T) for each s > -1/3, and global well-posedness for each s> -1/2.