Abstract
Hall-magnetohydrodynamic (Hall-MHD) equations which can be derived from two fluids model or kinetic models [see Acheritogaray et al. (Kinet Relat Models 4:901–918, 2011)] plays a crucial role in the study of magnetic reconnection in space plasmas, star formation, neutron stars. In this paper, we obtain two Fujita–Kato type results for the 3D Hall-MHD equations, which almost give positive answers to the question proposed by Chae and Lee (Remark 2 in Chae and Lee [J Differ Equ 256:3835–3858, 2014)]. The coupling between u and B is the main difficulty. Our idea is splitting the Navier–Stokes equations from the Hall-MHD equations and combining with some suitable blow-up criteria.
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