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Stability for the 3D generalized Hall‐MHD equations in the periodic domain

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  • Peng Wang
  • Zhengguang Guo
  • Shidi Zhou

Abstract

This paper studies stability of solutions for the 3D generalized incompressible Hall‐MHD Megnetohydrodynamics equations in the periodic domain T3${\mathbb {T}}^3$ with the magnetic field near a nontrivial equilibrium. Some new observations and estimates are implemented to exploit the enhanced dissipation produced by the nontrivial background magnetic field, which satisfies the Diophantine condition. Global stability and explicit time decay rates of solutions are shown.

Suggested Citation

  • Peng Wang & Zhengguang Guo & Shidi Zhou, 2025. "Stability for the 3D generalized Hall‐MHD equations in the periodic domain," Mathematische Nachrichten, Wiley Blackwell, vol. 298(12), pages 3714-3728, December.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:12:p:3714-3728
    DOI: 10.1002/mana.70062
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