This paper is concerned with the 2D magneto-micropolar equations with linear velocity damping and partial magnetic diffusion. We first examine that this system possesses a unique global smooth solution when the initial data is small. Moreover, we also study on the large-time behavior of these smooth solutions of the system. Under some new observation and rigorous analysis on the structure of the system, we establish the detail \(L^{2}\) decay estimates for solutions and high-order derivatives.

中文翻译：

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二维广义磁微极方程全局小解的存在性和时间衰减

本文主要研究具有线速度阻尼和局部磁扩散的二维磁微极方程。我们首先检查当初始数据很小时，该系统具有独特的全局平滑解。此外，我们还研究了系统这些光滑解的大时间行为。在对系统结构的一些新观察和严格分析下，我们建立了解和高阶导数的详细\(L^{2}\)衰减估计。