Almost conservation laws and global rough solutions to a Nonlinear Schrödinger equation

Mathematics – Analysis of PDEs

Scientific paper

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21 pages

Scientific paper

We prove an "almost conservation law" to obtain global-in-time well-posedness
for the cubic, defocussing nonlinear Schr\"odinger equation in H^s(R^n) when n
= 2, 3 and s > 4/7, 5/6, respectively.

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