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<p>We introduce a notion of a global weak solution to the incompressible magnetohydrodynamics (MHD) system with initial values in the Lorentz space <i>L</i><sup>3,∞</sup>(ℝ<sup>3</sup>), and demonstrate that this weak solution is stable with respect to the weak-* convergence of initial conditions. To do this, we employ splitting arguments in Lorentz spaces, which enables us to address the challenges arising from the low regularity of the Lorentz space <i>L</i><sup>3,∞</sup>(ℝ<sup>3</sup>). As an application of the stability property, we construct a large global weak solution to the incompressible MHD system with initial values in the Lorentz space <i>L</i><sup>3,∞</sup>(ℝ<sup>3</sup>). Besides, the uniqueness of this weak solution is established under certain constraints.</p>

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Global weak L3,∞-solution theory to the incompressible MHD system and applications

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Baishun Lai,
  • Xinlong Li,
  • Shihao Zhang

摘要

We introduce a notion of a global weak solution to the incompressible magnetohydrodynamics (MHD) system with initial values in the Lorentz space L3,∞(ℝ3), and demonstrate that this weak solution is stable with respect to the weak-* convergence of initial conditions. To do this, we employ splitting arguments in Lorentz spaces, which enables us to address the challenges arising from the low regularity of the Lorentz space L3,∞(ℝ3). As an application of the stability property, we construct a large global weak solution to the incompressible MHD system with initial values in the Lorentz space L3,∞(ℝ3). Besides, the uniqueness of this weak solution is established under certain constraints.