Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 42, pp. 1-23.

Title: Global well-posedness for Schrodinger equations with derivative 
       in a nonlinear term and data in low-order Sobolev spaces
        
Author: Hideo Takaoka (Hokkaido Univ., Japan)

Abstract: 
 In this paper, we study the existence of global solutions 
 to Schrodinger equations in one space dimension with a 
 derivative in a nonlinear term.  For the Cauchy problem 
 we assume that the data  belongs to a Sobolev space 
 weaker than the finite energy space $H^1$.
 Global existence for $H^1$ data follows from the 
 local existence and the use of a conserved quantity. 
 For $H^s$ data with $s<1$, the  main idea is to use a conservation 
 law and a frequency decomposition of the Cauchy data then follow
 the method introduced by Bourgain [3].
 Our proof relies on a generalization of the tri-linear estimates
 associated  with the Fourier restriction norm method used 
 in [1,25].
  
Submitted March 15, 2000. Published June 5, 2001.
Math Subject Classifications: 35Q55.
Key Words: Nonlinear Schrodinger equation; well-posedness.