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<p>In this paper, we study the mild ill-posedness problem of the two-dimensional MHD-Boussinesq system with the temperature-dependent thermal diffusivity and electrical conductivity near the background magnetic field in <i>L</i><sup>∞</sup>. Here we construct a sequence of initial data so that the <i>L</i><sup>∞</sup>-norm of vorticity of the corresponding solution is mildly ill-posed.</p>

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Mild Ill-posedness for the 2D MHD-Boussinesq System with a Background Magnetic Field

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • Haigen Wu,
  • Yue Li

摘要

In this paper, we study the mild ill-posedness problem of the two-dimensional MHD-Boussinesq system with the temperature-dependent thermal diffusivity and electrical conductivity near the background magnetic field in L∞. Here we construct a sequence of initial data so that the L∞-norm of vorticity of the corresponding solution is mildly ill-posed.