# 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}
}
• Published 2 October 2001
• Mathematics
• SIAM J. Math. Anal.
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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