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# Mathematical Research Letters

## Volume 9 (2002)

### Number 5

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

Pages: 659 – 682

DOI: http://dx.doi.org/10.4310/MRL.2002.v9.n5.a9

#### Authors

#### Abstract

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.