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Non-integer power estimate in modulation spaces and its applications

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Abstract

We give a method to estimate non-integer power function |u|k u in modulation space which is an open question in the study of modulation space. As an application, we can study Cauchy problem for the nonlinear Klein-Gordon equation with nonlinear term |u|k u in modulation space, where k is not an integer. Moreover, we also study the global solution with small initial value for the Klein-Gordon-Hartree equation. The results show some advantages of modulation space both in high and low regularity cases.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11671363 and 11471288) and Natural Science Foundation of Zhejiang Province (Grant No. LQ15A010003).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    JieCheng Chen, Qiang Huang & XiangRong Zhu

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  1. JieCheng Chen
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  2. Qiang Huang
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  3. XiangRong Zhu
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Correspondence to Qiang Huang.

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Chen, J., Huang, Q. & Zhu, X. Non-integer power estimate in modulation spaces and its applications. Sci. China Math. 60, 1443–1460 (2017). https://doi.org/10.1007/s11425-016-9023-y

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  • DOI: https://doi.org/10.1007/s11425-016-9023-y

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