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<p>In this paper, we consider the three-dimensional anisotropic incompressible magneto-hydrodynamics system on the periodic domain <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {T}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> with one large vertical viscosity and no vertical magnetic resistivity. We obtain the global well-posedness of the corresponding system with the initial data that verifies an anisotropic smallness condition. We also find that the strong vertical viscosity in the velocity equation can provide a regularizing effect both on the velocity field and the spatial average part of the magnetic field.</p>

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Global regularity of 3D incompressible MHD system with large vertical viscosity and no vertical magnetic resistivity on \(\mathbb {T}^3\)

  • 期刊论文

  • 发表日期：

    2026年3月21日

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  • Nacer Aarach,
  • Zhibin Wang,
  • Ning Zhu

摘要

In this paper, we consider the three-dimensional anisotropic incompressible magneto-hydrodynamics system on the periodic domain \(\mathbb {T}^3\) T 3 with one large vertical viscosity and no vertical magnetic resistivity. We obtain the global well-posedness of the corresponding system with the initial data that verifies an anisotropic smallness condition. We also find that the strong vertical viscosity in the velocity equation can provide a regularizing effect both on the velocity field and the spatial average part of the magnetic field.