In this paper we concern ourselves with an incompressible, viscous, isotropic, and periodic micropolar fluid. We find that in the absence of forcing and microtorquing there exists an infinite family of well-behaved solutions, which we call potential microflows, in which the fluid velocity vanishes identically, but the angular velocity of the microstructure is conservative and obeys a linear parabolic system. We then prove that nearby each potential microflow, the nonlinear equations of motion are well-posed globally-in-time, and solutions are stable. Finally, we prove that in the absence of force and microtorque, solutions decay exponentially, and in the presence of force and microtorque obeying certain conditions, solutions have quantifiable decay rates.

中文翻译：

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微极性流体的分析：潜在的微流解决方案的存在，附近的全局良好的位置和渐近稳定性

在本文中，我们关注的是不可压缩，粘性，各向同性和周期性的微极性流体。我们发现，在没有强迫和微扭转的情况下，存在着一系列行为良好的解决方案，我们称其为潜在的微流，其中流体速度相同地消失，但是微结构的角速度是保守的并且服从线性抛物线系统。然后，我们证明在每个潜在的微流附近，非线性运动方程在时间上全局定位正确，并且解是稳定的。最后，我们证明了在没有力和微转矩的情况下，溶液呈指数衰减，而在有力和微转矩的情况下服从某些条件，溶液具有可量化的衰减率。