The magnetohydrodynamics system consists of a coupling of the Navier-Stokes equations and Maxwell’s equation from electromagnetism. We extend the work of [2] on the Navier-Stokes equations to the magnetohydrodynamics system to prove its global well-posedness with logarithmically supercritical dissipation and diffusion with the logarithmic power that is improved in contrast to the previous work of [14]. The main difficulty is that the method in [2] relies heavily on the symmetry within the Navier-Stokes equation, which is lacking in the magnetohydrodynamics system due to the non-linear terms that are mixed with both velocity and magnetic fields; this difficulty may be overcome by somehow taking advantage of the symmetry within the energy formulation of the magnetohydrodynamics system appropriately.

中文翻译：

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具有改进对数幂的对数超临界 MHD 系统的全局规律性

磁流体动力学系统由纳维-斯托克斯方程和来自电磁学的麦克斯韦方程的耦合组成。我们将 [2] 在 Navier-Stokes 方程上的工作扩展到磁流体动力学系统，以证明其具有对数超临界耗散和扩散的全局适定性，其对数幂与 [14] 的先前工作相比有所改进。主要困难是[2]中的方法严重依赖于纳维-斯托克斯方程中的对称性，由于非线性项与速度和磁场混合，磁流体动力学系统中缺乏这种对称性；这个困难可以通过适当利用磁流体动力学系统能量公式中的对称性来克服。