In this paper, we investigate the initial value problem for the 3D magneto-micropolar fluid equations with mixed partial viscosity. The main purpose of this paper is to establish global well-posedness of classical small solutions. More precisely, we prove that the global stability of perturbations near the steady solution is given by a background magnetic field. The proof is mainly based on the energy estimate and bootstrapping argument.

中文翻译：

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具有接近平衡的混合部分粘度的3D磁-微极性流体方程的整体适定性

在本文中，我们研究了具有部分混合粘度的3D磁微极性流体方程的初值问题。本文的主要目的是建立经典小解的全局适定性。更确切地说，我们证明了稳定磁场附近摄动的整体稳定性由背景磁场给出。证明主要基于能量估计和自举参数。