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Scattering Versus Blowup Beyond the Mass-Energy Threshold for the Davey-Stewartson Equation in ℝ3

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Abstract

We study the Cauchy problem for the Davey-Stewartson equation

$${\rm{i}}{\partial _t}u + \Delta u + {\left| u \right|^2}u + {E_1}({\left| u \right|^2})u = 0,\,\,\,\,\,\,(t,x) \in \mathbb{R} \times {\mathbb{R}^3}.$$

The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u0)E(u0) above the ground state threshold M(Q)E(Q).

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Acknowledgements

The authors thank the referees for careful reading of the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics & Fujian Key Laboratory of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou, 350117, P. R. China

    Yan Fang Gao & Zhi Yong Wang

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  1. Yan Fang Gao
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  2. Zhi Yong Wang
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Correspondence to Yan Fang Gao.

Additional information

Supported by Natural Science Foundation of China (Grant Nos. 11501111, 11771082 and 11601082), China Scholarship Council (Grant No. 201808350018) and Foundation of the Science and Technology Department of Fujian Province (Grant No. 2017J05002)

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Gao, Y.F., Wang, Z.Y. Scattering Versus Blowup Beyond the Mass-Energy Threshold for the Davey-Stewartson Equation in ℝ3. Acta. Math. Sin.-English Ser. 37, 1415–1436 (2021). https://doi.org/10.1007/s10114-021-0354-1

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  • DOI: https://doi.org/10.1007/s10114-021-0354-1

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