Abstract
A one-component regularity criterion for the non-resistive axially symmetric Hall-MHD system is given in this paper. More precisely, we show that strong solutions to a family of axially symmetric initial data, whose velocity and current density have trivial swirl components, could be smoothly extended beyond a possible blow-up time \(T_{*}\) if and only if the swirl component of the magnetic field \(h_{\theta }\) satisfies a Beale-Kato-Majda-type criterion. See (1.5) below. This criterion is not trivial even if the velocity field vanishes since the quantity \(\frac{h_{\theta }}{r}\) satisfies a partial Burgers’ equation in this situation.
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Acknowledgements
We wish to express our gratitude to anonymous referees for their helpful suggestions on this work.
The first author is supported by Natural Science Foundation of Jiangsu Province (No. BK20200803) and National Natural Science Foundation of China (No. 12001285).
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Li, Z., Yang, M. On a Single-Component Regularity Criterion for the Non-resistive Axially Symmetric Hall-MHD System. Acta Appl Math 181, 1 (2022). https://doi.org/10.1007/s10440-022-00519-5
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DOI: https://doi.org/10.1007/s10440-022-00519-5