论文标题
微极流体的分析：潜在的微流溶液的存在，附近的全球良好性和渐近稳定性
Analysis of micropolar fluids: existence of potential microflow solutions, nearby global well-posedness, and asymptotic stability
论文作者
论文摘要
在本文中，我们以不可压缩，粘性，各向同性和周期性的微极液为担心。我们发现，在没有强迫和微音阶的情况下，存在一个无限的溶液家族，我们称之为潜在的微滴管，其中流体速度相同消失，但是微观结构的角速度是保守的，并且遵守线性寄生虫系统。然后，我们证明在每个电势微流附近，非线性运动方程式是全球范围很好的，溶液是稳定的。最后，我们证明，在没有力和微型脉冲的情况下，溶液呈指数衰减，并且在存在力和微观的存在下，溶液具有可量化的衰减速率。
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.
