Global Well-Posedness for the 3D Incompressible Hall-Magnetohydrodynamic Equations with Fujita–Kato Type Initial Data
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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.
KeywordsHall-MHD equations Fujita–Kato Global well-posedness
Mathematics Subject Classification35Q35 35B40 35B65 76W05
The authors thank the referee for the careful reading and helpful comments. Wan was supported by the NSF of the Jiangsu Higher Education Institutions of China (18KJB110018), the NSF of Jiangsu Province (BK20180721). Zhou was supported by NSFC (No. 11171154).
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Conflict of interest
The authors declare that they have no conflict of interest.
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