Energy and local energy bounds for the 1-D cubic NLS equation in
- Author(s): Koch, H
- Tataru, D
- et al.
We consider the cubic Nonlinear Schroedinger Equation (NLS) in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time Hs bounds in terms of the Hs size of the initial data for s >=-1/4 . This improves earlier results of Christ-Colliander-Tao  and of the authors . The new ingredients are a localization in space and local energy decay, which we hope to be of independent interest.
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