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arXiv · 1508.07298

The defocusing quintic NLS in four space dimensions

Benjamin Dodson·Changxing Miao·Jason Murphy·Jiqiang Zheng
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Abstract

We consider the defocusing quintic nonlinear Schrödinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be global and scatter. We employ a space-localized interaction Morawetz inequality, the proof of which requires us to overcome the logarithmic failure in the double Duhamel argument in four dimensions.

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Benjamin Dodson, Changxing Miao, Jason Murphy, Jiqiang Zheng. 2015-08-28. The defocusing quintic NLS in four space dimensions. https://arxiv.org/abs/1508.07298

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