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

J. Colliander·M. Keel·G. Staffilani·H. Takaoka·T. Tao
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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.

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J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao. 2002-03-21. Almost conservation laws and global rough solutions to a Nonlinear Schrödinger equation. https://arxiv.org/abs/math/0203218

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