Abstract
In this paper, we consider the global well-posedness of the incompressible Hall-MHD equations in \({\mathbb {R}}^3\). We prove that the solution of this system is globally regular if the initial data is axisymmetric and the swirl components of the velocity and magnetic vorticity are trivial. It should be pointed out that the initial data can be arbitrarily large and satisfy low regularity assumptions.
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Acknowledgements
The authors would like to thank Professor Guilong Gui for some valuable comments and helpful discussions. This work was partially supported by the National Natural Science Foundation of China under the grants 11931013, 12201491, 11801443, and 12271031 and the Scientific Research Plan Projects of Shaanxi Education Department under the grant 22JK0475.
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Communicated by David Lannes.
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Li, Z., Liu, P. Global regularity for the 3D Hall-MHD equations with low regularity axisymmetric data. Monatsh Math 201, 173–195 (2023). https://doi.org/10.1007/s00605-022-01795-x
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DOI: https://doi.org/10.1007/s00605-022-01795-x