On the well-posedness and temporal decay for the 3D generalized incompressible Hall-MHD system

  • Xiaopeng Zhao
  • Mingxuan ZhuEmail author


In this paper, we prove a new result on the properties of decay character \(r^*\) (see Lemma 2.6) and then show a small data global well-posedness result for three-dimensional generalized incompressible Hall-MHD system. In the end, through Fourier splitting method, the properties of decay character \(r^*\) and mathematical induction, we study the decay rate of higher-order spatial and time derivatives of strong solutions to such system.


Generalized Hall-MHD equations Decay rate Decay character Mathematical induction 

Mathematics Subject Classification

35B40 35Q35 74W05 



The authors are indebted to anonymous referees for their helpful comments. This work was partially supported by Natural Science Foundation of Anhui Province Higher School (Grant No: KJ2017A622) and National Natural Science Foundation of China (Grant No. 11771183).


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.College of ScienceNortheastern UniversityShenyangChina
  2. 2.School of Mathematical SciencesQufu Normal UniversityQufuChina

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