Abstract
In this paper, we consider the Cauchy problem of the multi-dimensional generalized MHD system in the whole space and construct global smooth solutions with a class of large initial data by exploring the structure of the nonlinear term. Precisely speaking, our choice of special initial data whose \(L^{\infty }\) norm can be arbitrarily large allows to generate a unique global-in-time solution to the generalized MHD system.
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Acknowledgements
The authors want to thank the referees for their constructive comments and helpful suggestions which greatly improved the presentation of this paper. J. Li is supported by the National Natural Science Foundation of China (Grant No. 11801090) and Postdoctoral Science Foundation of China (2020T130129 and 2020M672565). Y. Yu is supported by the Natural Science Foundation of Anhui Province (No. 1908085QA05) and the PhD Scientific Research Start-up Foundation of Anhui Normal University.
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Li, J., Yu, Y. Global Smooth Solutions of the Generalized MHD Equations with Large Initial Data. Results Math 76, 61 (2021). https://doi.org/10.1007/s00025-021-01373-x
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DOI: https://doi.org/10.1007/s00025-021-01373-x