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Global Well-Posedness for the 3D Incompressible Hall-Magnetohydrodynamic Equations with Fujita–Kato Type Initial Data

  • Renhui Wan
  • Yong ZhouEmail author
Article
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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.

Keywords

Hall-MHD equations Fujita–Kato Global well-posedness 

Mathematics Subject Classification

35Q35 35B40 35B65 76W05 

Notes

Acknowledgements

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).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics School of Mathematical SciencesNanjing Normal UniversityNanjingPeople’s Republic of China
  2. 2.School of Mathematics (Zhuhai)Sun Yat-Sen UniversityZhuhaiPeople’s Republic of China
  3. 3.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China

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