A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative

@article{Colliander2002ARG,
  title={A Refined Global Well-Posedness Result for Schr{\"o}dinger Equations with Derivative},
  author={James E. Colliander and Markus Keel and Gigliola Staffilani and Hideo Takaoka and Terence Tao},
  journal={SIAM J. Math. Anal.},
  year={2002},
  volume={34},
  pages={64-86}
}
In this paper we prove that the one-dimensional Schrodinger equation with derivative in the nonlinear term is globally well-posed in Hs for $s > \frac12$ for data small in L2 . To understand the strength of this result one should recall that for $s \frac23$. The same argument can be used to prove that any quintic nonlinear defocusing Schrodinger equation on the line is globally well-posed for large data in Hs for $s>\frac12$. 
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