J. Colliander

Learn More
We prove that the 1D Schrödinger 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 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(More)
In this paper we prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in H s , for s > 1 2 for data small in L 2. To understand the strength of this result one should recall that for s < 1 2 the Cauchy problem is ill-posed, in the sense that uniform continuity with respect to the initial data fails. The result(More)
  • 1