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引用
期刊论文
The defocusing energy- supercritical NLS in four space dimensions,
J. Functional Analysis,2014,267(2):1662–1724 | 2014年09月25日 | 10.1016/j.jfa.2014.06.016
We consider a class of defocusing energy-supercritical nonlinear Schr\"odinger equations in four space dimensions. Following a concentration-compactness approach, we show that for $1<s_c<3/2$, any solution that remains bounded in the critical Sobolev space $\dot{H}_x^{s_c}(\R^4)$ must be global and scatter. Key ingredients in the proof include a long-time Strichartz estimate \`a la Dodson and a frequency-localized interaction Morawetz inequality.
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