A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces
Herbert Koch, Daniel Tataru
Abstract
We consider the cubic Nonlinear Schrodinger Equation 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 greater than or equal to -1/6.
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