We study the global well‐posedness and existence of uniform attractor for magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier–Stokes equations for the fluid velocity and pressure coupled with a reduced from of the Maxwell equations for the magnetic field. The fluid velocity is assumed to satisfy a no‐slip boundary condition, while the magnetic field is subject to a time‐dependent Dirichlet boundary condition. We first establish the global existence of weak and strong solutions to Equations (1.1)‐(1.4). And at this stage, we further derive the existence of a uniform attractor for Equations (1.1)‐(1.4).

中文翻译：

---

磁流体动力学方程的整体适定性和均匀吸引子的存在

我们研究了磁流体动力学（MHD）方程的整体适定性和均匀吸引子的存在性。流体力学系统由用于流体速度和压力的Navier–Stokes方程以及与磁场的Maxwell方程的简化组成。假定流体速度满足无滑移边界条件，而磁场则受时间相关的狄利克雷边界条件的影响。我们首先建立方程（1.1）-（1.4）的弱解和强解的全局存在性。在这一阶段，我们进一步推导了方程（1.1）-（1.4）的统一吸引子的存在。