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

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Abstract

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.

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Acknowledgements

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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Correspondence to Mingxuan Zhu.

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Zhao, X., Zhu, M. On the well-posedness and temporal decay for the 3D generalized incompressible Hall-MHD system. Z. Angew. Math. Phys. 71, 27 (2020) doi:10.1007/s00033-020-1249-1

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Keywords

  • Generalized Hall-MHD equations
  • Decay rate
  • Decay character
  • Mathematical induction

Mathematics Subject Classification

  • 35B40
  • 35Q35
  • 74W05