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

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)

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.

Full Text (PDF format)