Sharp Criteria of Scattering for the Fractional NLS

Qing Guo; Shihui Zhu

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arXiv · 1706.02549

Sharp Criteria of Scattering for the Fractional NLS

Qing Guo·Shihui Zhu

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Abstract

In this paper, the sharp threshold of scattering for the fractional nonlinear Schr\"{o}dinger equation in the $L^2$-supercritical case is obtained, i.e., if $1+\frac{4s}{N} M[Q]^{\frac{s-s_c}{s_c}}\| Q\|^2_{\dot H^s},$$ then the corresponding solution $u(t)$ blows up in finite time, according to Boulenger, Himmelsbach, and Lenzmann's results in [2].

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Qing Guo, Shihui Zhu. 2017-06-07. Sharp Criteria of Scattering for the Fractional NLS. https://arxiv.org/abs/1706.02549

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