Abstract
In this paper we derive the global existence of smooth solutions to the 3D generalized Hall-MHD equations for a class of large initial data, whose \(L^{\infty }\) norms can be arbitrarily large. In addition, we give an example to show that such a large initial value does exist. Our idea is splitting the generalized heat equations from generalized Hall-MHD system to generate a small quantity for large time \(t\).
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Acknowledgements
The authors are very grateful to the referees for their detailed comments and valuable suggestions, which greatly improved the manuscript. The authors are grateful to Dr. Yanghai Yu for some useful suggestions. Y. Tang’s research was supported in part by the National Natural Science Foundation under Grant No. 11471129.
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Wu, X., Tang, Y. A Class of Large Solutions to the 3D Generalized Hall-MHD Equations. Acta Appl Math 169, 681–690 (2020). https://doi.org/10.1007/s10440-020-00318-w
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DOI: https://doi.org/10.1007/s10440-020-00318-w