In this paper, we study the thermally radiative magnetohydrodynamic equations in 3D, which describe the dynamical behaviors of magnetized fluids that have nonignorable energy and momentum exchange with radiation under the nonlocal thermal equilibrium case. By using exquisite energy estimate, global existence and uniqueness of classical solutions to Cauchy problem in or are established when initial data is a small perturbation of some given equilibrium. We can further prove that the rates of convergence of solution toward the equilibrium state are algebraic in and exponential in under some additional conditions on initial data. The proof is based on the Fourier multiplier technique.

中文翻译：

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3D中的热辐射磁流体动力学方程的整体适定性

在本文中，我们研究了3D中的热辐射磁流体动力学方程，该方程描述了在非局部热平衡情况下具有不可忽略的能量和与辐射交换的磁化流体的动力学行为。通过使用精致的能量估计，全球存在和经典解Cauchy问题的唯一性或当初始数据为某些给定的平衡的一个小扰动建立。我们可以进一步证明，在初始数据的某些附加条件下，溶液向平衡态的收敛速度是代数的，指数的是指数的。该证明基于傅立叶乘法器技术。