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On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect

Author

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  • Xiaopeng Zhao

    (College of Sciences, Northeastern University, Shenyang 110819, China)

Abstract

The main purpose of this paper is to study the global existence and uniqueness of solutions for three-dimensional incompressible magnetic induction equations with Hall effect provided that ∥ u 0 ∥ H 3 2 + ε + ∥ b 0 ∥ H 2 ( 0 < ε < 1 ) is sufficiently small. Moreover, using the Fourier splitting method and the properties of decay character r * , one also shows the algebraic decay rate of a higher order derivative of solutions to magnetic induction equations with the Hall effect.

Suggested Citation

  • Xiaopeng Zhao, 2020. "On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect," Mathematics, MDPI, vol. 8(10), pages 1-25, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1847-:d:431741
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    References listed on IDEAS

    as
    1. Fan, Jishan & Ahmad, Bashir & Hayat, Tasawar & Zhou, Yong, 2016. "On blow-up criteria for a new Hall-MHD system," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 20-24.
    2. X. H. Deng & H. Matsumoto, 2001. "Rapid magnetic reconnection in the Earth’s magnetosphere mediated by whistler waves," Nature, Nature, vol. 410(6828), pages 557-560, March.
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