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

Herbert Koch; Daniel Tataru

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

Analysis of PDEs 2007-05-25 v2

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

Keywords

cubic nonlinear schrodinger equation priori bounds negative sobolev spaces one space dimension initial data

Cite

@article{arxiv.math/0612717,
  title  = {A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces},
  author = {Herbert Koch and Daniel Tataru},
  journal= {arXiv preprint arXiv:math/0612717},
  year   = {2007}
}

Comments

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

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