Almost conservation laws and global rough solutions to a Nonlinear Schrödinger equation
arXiv:math/0203218
Abstract
We prove an "almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in H^s(R^n) when n = 2, 3 and s > 4/7, 5/6, respectively.
21 pages