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Global Well-posedness and Global Attractor for Two-dimensional Zakharov-Kuznetsov Equation

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Abstract

The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in Hs(ℝ2) for all \({\textstyle{5 \over 7}}\) < s < 1 via using I-method in the context of atomic spaces. By means of the increment of modified energy, the existence of global attractor for the weakly damped, forced Zakharov-Kuznetsov equation is also established in Hs(ℝ2) for \({\textstyle{{10} \over {11}}}\) < s < 1.

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Acknowledgements

The author would like to express his deep gratitude to Professor Yoshio Tsutsumi, Professor Baoxiang Wang and Professor Liqun Zhang for their guidance and help.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Min Jie Shan

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  1. Min Jie Shan
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Correspondence to Min Jie Shan.

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Supported by China Postdoctoral Science Foundation (Grant No. 2019M650872)

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Shan, M.J. Global Well-posedness and Global Attractor for Two-dimensional Zakharov-Kuznetsov Equation. Acta. Math. Sin.-English Ser. 36, 969–1000 (2020). https://doi.org/10.1007/s10114-020-9381-6

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  • DOI: https://doi.org/10.1007/s10114-020-9381-6

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