Global Well-posedness for the Defocusing, Quintic Nonlinear Schrodinger Equation in One Dimension for Low Regularity Data

In this paper, we prove global well-posedness of the one-dimensional quintic defocusing nonlinear Schrodinger initial value problem with low regularity initial data. We show that a unique global solution exists for u(0) is an element of H-s(R), s > 1/4. This improves the result in De Silva, Pavlovic, Staffilani, and Tzirakis [Global well-posedness and polynomial bounds for the defocusing L-2 -critical Schrodinger equation in R.], which proved global wellposedness for s > 1/3. The main new argument is that we obtain almost Morawetz estimates with an improved error.