Abstract
We establish regularity criteria of 3D axisymmetric non-resistive MHD system with non-zero swirl. It is shown that strong solutions of this system can be smoothly extended beyond the possible blow-up time \(T^*\) if the horizontal angular component of the velocity belongs to some Lorentz spaces. Our result does not need any additional assumption on the magnetic field. In particular, we also obtain regularity criteria for the 3D axisymmetric Navier-Stokes system.
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Acknowledgements
The authors thank Professor Guilong Gui for his helpful discussion, and thank the referees for their valuable comments on the initial manuscript. The work is partially supported by the National Natural Science Foundation of China (Program No. 12201491) and Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 22JK0475).
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Li, Z., Liu, W. Regularity Criteria for the 3D Axisymmetric Non-Resistive MHD System in Lorentz Spaces. Results Math 78, 86 (2023). https://doi.org/10.1007/s00025-023-01863-0
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DOI: https://doi.org/10.1007/s00025-023-01863-0