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Global well-posedness and scattering for the defocusing \(\dot H^s\)-critical NLS

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Abstract

The authors consider the scattering phenomena of the defocusing \(\dot H^s\)-critical NLS. It is shown that if a solution of the defocusing NLS remains bounded in the critical homogeneous Sobolev norm on its maximal interval of existence, then the solution is global and scatters.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310016, China

    Jian Xie

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310058, China

    Daoyuan Fang

Authors
  1. Jian Xie
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  2. Daoyuan Fang
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Corresponding author

Correspondence to Jian Xie.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10931007, 11226184, 11271322) and the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217).

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Xie, J., Fang, D. Global well-posedness and scattering for the defocusing \(\dot H^s\)-critical NLS. Chin. Ann. Math. Ser. B 34, 801–842 (2013). https://doi.org/10.1007/s11401-013-0808-6

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  • DOI: https://doi.org/10.1007/s11401-013-0808-6

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