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<p>This paper investigates global stability of the three-dimensional incompressible magnetic Bénard system with horizontal dissipation. The lack of dissipation in the vertical direction poses challenges for studying global stability. We first establish global stability of 3D magnetic Bénard system near the hydrostatic balance. Furthermore, the optimal time-decay rates of the global solution and its partial derivatives are established when the initial data also belongs to homogeneous negative Sobolev spaces.</p>

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Global Stability of 3D Magnetic Bénard System with Horizontal Dissipation Near the Hydrostatic Balance

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Yuzhu Wang,
  • Jingyi Zhang

摘要

This paper investigates global stability of the three-dimensional incompressible magnetic Bénard system with horizontal dissipation. The lack of dissipation in the vertical direction poses challenges for studying global stability. We first establish global stability of 3D magnetic Bénard system near the hydrostatic balance. Furthermore, the optimal time-decay rates of the global solution and its partial derivatives are established when the initial data also belongs to homogeneous negative Sobolev spaces.