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<p>This paper provides the stability analysis of 2D-generalized magnetohydrodynamic (MHD) equations with the mixed linear damping and partial dissipation in one direction. We establish the global existence for stable solution of the system near a background magnetic field by the bootstrap argument. In addition, the large-time decay rates of the first-order derivatives to the perturbed solution are also obtained by analyzing the structure of the system. These results rigorously confirm a nonlinear phenomenon observed in physical experiments, namely the stabilizing effect of external magnetic fields on conductive fluids.</p>

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Global stable solution and large-time decay of the 2D-generalized MHD equations near an equilibrium

  • 期刊论文

  • 发表日期：

    2025年12月26日

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  • Yana Guo,
  • Xiao Li,
  • Bo-Qing Dong

摘要

This paper provides the stability analysis of 2D-generalized magnetohydrodynamic (MHD) equations with the mixed linear damping and partial dissipation in one direction. We establish the global existence for stable solution of the system near a background magnetic field by the bootstrap argument. In addition, the large-time decay rates of the first-order derivatives to the perturbed solution are also obtained by analyzing the structure of the system. These results rigorously confirm a nonlinear phenomenon observed in physical experiments, namely the stabilizing effect of external magnetic fields on conductive fluids.