GLOBAL WELL-POSEDNESS FOR SCHR ¨ ODINGER EQUATIONS WITH DERIVATIVE ∗

By James E. Colliander, Markus Keel, Gigliola Staffilani, Hideo Takaoka, Terence Tao. 2001

85 citations recorded by the source corpus.

We prove that the one-dimensional Schrodinger equation with derivative in the nonlinear term is globally well-posed in H s for s> 2/3, for small L 2 data. The result follows from an application of the "I-method." This method allows us to define a modification of the energy norm H 1 that is "almost conserved" and can be used to perform an iteration argument. We also remark that 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 H s , for s> 2/3.

View Paper: https://www.semanticscholar.org/paper/811bd76e8da3c2f59042b93f1ac60c13a1ce180f

Citations in the corpus

• Well-posedness for a generalized derivative nonlinear Schrödinger equation (2016, unknown): “, [3], Solutions of low regularity have been studied in [21] [4], [13], [7].”