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On global existence for mass-supercritical nonlinear fractional Hartree equations

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Abstract

In this paper, we consider the nonlinear fractional Schrödinger equations with Hartree type nonlinearity in mass-supercritical and energy-subcritical case. By sharp Hardy-Littlewood-Sobolev inequality and the Pohozaev identity, we established a threshold condition, which leads to a global existence of solutions in energy space.

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Acknowledgements

The author is very grateful to Professor Daomin Cao for helpful discussions and suggestions. The author would also like to thank the anonymous referee for valuable comments.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Dan Wu

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  1. Dan Wu
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Correspondence to Dan Wu.

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Supported by the National Center of Mathematics and Interdisciplinary Sciences, CAS.

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Wu, D. On global existence for mass-supercritical nonlinear fractional Hartree equations. Acta Math. Appl. Sin. Engl. Ser. 33, 389–400 (2017). https://doi.org/10.1007/s10255-017-0668-z

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  • DOI: https://doi.org/10.1007/s10255-017-0668-z

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