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

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

References in corpus (1)

• Global well-posedness for KdV in Sobolev Spaces of negative index

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