微极流体方程可以描述悬浮液、动物血液和液晶等多种复杂流体的流动现象，在科学研究和实际生产中均有重要的意义。许多学者在研究微极流体方程时，引入了非线性阻尼项以描述流体粒子在流动过程中的阻力和摩擦效应。为了使微极流体方程的结论更具广泛应用性，本文旨在拓宽阻尼项参数 的范围对三维非线性阻尼微极流体方程解的衰减性进行研究，主要研究内容如下： 针对不含外力项的三维非线性阻尼微极流体方程解的衰减性，首先通过对微极流体方程组的第一个方程和第二个方程的耦合得到方程对应的能量不等式，并给出 和 时强解的存在性定理；其次，分别使用逐项估计法和矩阵估计法克服了非线性项 和 的困难，利用各种基本不等式对方程变换后的各项进行了先验估计，并使用Fourier分解方法和Plancherel定理对方程解和解的梯度进行了衰减估计，得到了 在不同范围内的一致衰减率；最后借助于Duhamel原理对旋转场的衰变做出了进一步改进。 针对含外力项的三维非线性阻尼微极流体方程解的衰减性，基于本文第三部分的衰减性结论，提出了外力假设条件Ⅰ、Ⅱ，并结合外力假设条件与其他项的估计，推导得出了含外力项时方程解的一致衰减率；此外，给出了外力的梯度假设条件Ⅲ，对时间 进行限制得到了方程解的梯度是单调递减函数；最后，经过改进得到了含外力项旋转场的衰减估计。 针对三维非线性阻尼微极流体方程解的渐近稳定性，本文引入了在任意初始扰动条件下的扰动方程，然后对扰动方程与原始方程作差，同样使用矩阵估计法和Fourier分解方法对作差后的方程进行了深入讨论，证明了扰动解渐近收敛于原始解，并得出了相应的一致衰减率。

The micropolar fluid equation can describe the flow phenomena of various complex fluids such as suspension, animal blood and liquid crystal, which is of great significance in scientific research and practical production. In the study of micropolar fluid equations, many scholars have introduced nonlinear damping terms to describe the resistance and friction effects of fluid particles in the flow process. In order to make the conclusion of the micropolar fluid equation more widely applicable, this paper aims to broaden the range of damping parameters  to study the decay of the solution of the three-dimensional nonlinear damped micropolar fluid equation. The main research contents are as follows:

For the decay of the solutions of the three-dimensional nonlinear damped micropolar fluid equations without external force terms, firstly, the energy inequality corresponding to the equation is obtained by coupling the first equation and the second equation of system , as well as the existence theorems of the strong solutions when  and  are given. Secondly, the term by term and matrix estimation methods are used to overcome the difficulties of the nonlinear terms  and , respectively, and the transformed terms of the equations are estimated a priori by using the various basic inequalities, and the gradients of the solutions of the equations and the solutions are estimated at a decay rate in different ranges by using Fourier decomposition methods and Plancherel's theorem. The decay of the gradient of the equation solution is estimated using the Fourier decomposition method and Plancherel's theorem, and the consistent decay rate of  in different ranges is obtained. Finally, the decay of the rotating field is further improved with the help of Duhamel's principle.

For the decay of the three-dimensional nonlinear damped micropolar fluid equation solutions containing external force terms, based on the decay estimates from the third section, we propose external force assumption conditions Ⅰ and Ⅱ. By coupling these external force assumption conditions with the estimates of other terms, we derive a uniform decay rate for the solutions of the equations with external force terms. Additionally, we present the gradient assumption condition Ⅲ for the external force, and by imposing time restrictions, we demonstrate that the gradient of the solution is a monotonically decreasing function. Finally, we improve the decay estimate for the rotating field with external force terms.

For the asymptotic stability of the solutions of the three-dimensional nonlinear damped micropolar fluid equations, this paper introduces the perturbation equation under any initial perturbation condition, and then makes a difference between the perturbation equation and the original equation. The matrix estimation method and Fourier decomposition method are also used to discuss the difference equation in depth. It is proved that the perturbation solution converges asymptotically to the original solution, and the corresponding uniform decay rate is obtained.

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