Beale–Kato–Majda Regularity Criterion of Smooth Solutions for the Hall-MHD Equations with Zero Viscosity

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 B˙∞,∞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). © 2021, Sociedade Brasileira de Matemática.