Mathematical Research Letters

Volume 9, Issue 5, September 2002 pp. 659-682.

Almost Conservation Laws and Global Rough Solutions to a Nonlinear Schrödinger Equation

Authors: J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao
Author institution: University of Toronto, University of Minnesota Twin Cities, Stanford University, Hokkaido University, and University of California Los Angeles

Summary: We prove an ``almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in $H^s({\mathbb{R}}^n)$ when $n = 2,3$ and $s > \frac{4}{7}, \frac{5}{6}$, respectively.

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