Mathematical Research Letters

Volume 9 (2002)

Number 5

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

Pages: 659 – 682



J. Colliander (University of Toronto)

M. Keel (University of Minnesota Twin Cities)

G. Staffilani (Stanford University)

H. Takaoka (Hokkaido University)

T. Tao (University of California at Los Angeles)


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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