Abstract
In this paper, we investigate the Cauchy problem for the 3D incompressible Hall-MHD equations with zero viscosity. We prove the Beale–Kato–Majda regularity criterion of smooth solutions in terms of the velocity field and magnetic field in the homogeneous Besov spaces \({\dot{B}}_{\infty ,\infty }^{0} \). Then we give a criterion on extension beyond T of our local solution. Our result may be also regarded as an extension of the corresponding result of Wang and Zuo (Commun Pure Appl Anal 13:1327–1336, 2014).
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Acknowledgements
The authors would like to thank the referees for valuable comments and suggestions for improving this paper. Part of the work was carried out while S. Gala was a long-term visitor at the University of Catania. The hospitality of Catania University is graciously acknowledged. This research is partially supported by Piano della Ricerca 2016-2018—Linea di intervento 2: “Metodi variazionali ed equazioni di erenziali”. This paper has been supported by the RUDN University Strategic Academic Leadership Program ”. The authors are indebted with Prof. Yong Zhou for having drawn his attention to the above problem and for useful discussions.
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Gala, S., Galakhov, E., Ragusa, M.A. et al. Beale–Kato–Majda Regularity Criterion of Smooth Solutions for the Hall-MHD Equations with Zero Viscosity. Bull Braz Math Soc, New Series 53, 229–241 (2022). https://doi.org/10.1007/s00574-021-00256-7
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DOI: https://doi.org/10.1007/s00574-021-00256-7