Abstract
Under the condition of small external forces, we obtain existence of a weak solution of the steady Hall-MHD system with Hölder continuous magnetic field. We also established regularity of weak solutions provided that magnetic fields are bounded. For sufficiently small external forces, uniqueness result is also established.
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Acknowledgements
The authors are grateful to their supervisor, Prof. Xingbin Pan, for guidance and constant encouragement. The referee is thanked for valuable comments and suggestions that have improved the manuscript. This work was partially supported by the National Natural Science Foundation of China Grant Nos. 11671143 and 11901003. Zeng was partially supported by the Natural Science Foundation of Chongqing Grant No. cstc2019jcyj-msxmX0214, the Science and Technology Research Program of Chongqing Municipal Education Commission Grant No. KJQN201800841, the Research Program of CTBU Grant No. 1952042 and the Program for the Introduction of High-Level Talents of CTBU Grant No. 1856013. Zhang was also supported by Anhui Provincial Natural Science Foundation Grant No. 1908085QA28.
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Zeng, Y., Zhang, Z. Existence, regularity and uniqueness of weak solutions with bounded magnetic fields to the steady Hall-MHD system. Calc. Var. 59, 84 (2020). https://doi.org/10.1007/s00526-020-01745-1
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DOI: https://doi.org/10.1007/s00526-020-01745-1