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<p>This paper focuses on the stability of the 3D anisotropic incompressible magnetohydrodynamic (MHD) system with partial and fractional dissipation near a background magnetic field. We obtain the global well-posedness of the solutions, provided that the <i>H</i><sup>2</sup>(ℝ<sup>3</sup>) norm of initial datum is sufficiently small. Due to the emergence of fractional dissipation, some conventional energy estimate methods are no longer applicable. To overcome this challenge, we establish new fractional anisotropic inequalities, which play a crucial role in bounding the nonlinear terms by the dissipative parts. Our result extends some existing conclusions.</p>

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Global solution to the 3D anisotropic incompressible MHD system with partial and fractional dissipation

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Yanping Zhou,
  • Pingping Gui,
  • Huiyang Song

摘要

This paper focuses on the stability of the 3D anisotropic incompressible magnetohydrodynamic (MHD) system with partial and fractional dissipation near a background magnetic field. We obtain the global well-posedness of the solutions, provided that the H2(ℝ3) norm of initial datum is sufficiently small. Due to the emergence of fractional dissipation, some conventional energy estimate methods are no longer applicable. To overcome this challenge, we establish new fractional anisotropic inequalities, which play a crucial role in bounding the nonlinear terms by the dissipative parts. Our result extends some existing conclusions.