A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces

Details A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces

2006-12-22

arxiv.org/abs/math/0612717v2

Mathematics

Analysis of PDEs

27 pages very minor misprints corrected (see formulas (4), (7))

Scientific paper

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 H^s bounds in terms of the H^s size of the initial data for s
greater than or equal to -1/6.

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