微极流方程描述了一类包含微旋转效应和惯性力的非牛顿流体运动，能较好地表征一些经典的Navier-Stokes模型无法描述的不可压缩流体动力学行为. 近年来，微极流方程的理论研究成为偏微分方程领域的热点内容，本文将对三维微极流方程解的渐近性态，尤其是解的一致吸引子的存在性进行讨论，并探讨解对部分系数的连续依赖性问题. 主要研究内容如下：
研究了具有非线性阻尼项的三维微极流方程一致吸引子的存在性. 首先，当参数3<β<5，初值(u_τ,ω_τ)∈V₁xV₂和外力(f₁,f₂)∈ℋ(f₁⁰)xℋ(f₂⁰) 时，对方程解进行一系列一致估计证明了过程{U(f₁,f₂)(t,τ)}_t≥τ在空间((V₁xV₂)x(ℋ(f₁⁰)xℋ(f₂⁰)),V₁xV₂)是连续的，并应用过程理论得到(V₁xV₂ ,V₁xV₂)一致吸引子的存在性. 进一步证明了过程{U(f₁,f₂)(t,τ)}t≥τ 是(V₁xV₂,^₂(Ω)x²(Ω))一致紧的. 并因此得到 (V₁xV₂,^₂(Ω)x^₂(Ω))一致吸引子的存在性，最后运用反证法证明了(V₁xV₂ ,V₁xV₂)一致吸引子实际上是(V₁xV₂,^₂(Ω)x^₂(Ω))的一致吸引子.
讨论了三维非线性阻尼微极流方程解对部分系数的连续依赖性. 首先利用一致吸引子中对方程解的一致估计. 其次，借助先验估计，运用三线性不等式、Gagliardo-Nirenberg不等式和Gronwall不等式获得方程解的差的范数所满足的微分不等式. 最终得到微极流方程的解关于初值及系数ν,κ,γ的连续依赖性结论.

The micropolar flow equations describe the motion of a class of non-Newtonian fluids containing micro-rotational effects and inertial forces, and can better characterize the dynamical behavior of some incompressible fluids that cannot be described by the classical Navier-Stokes model. The mathematical theory of this model has been a hot research topic in the field of partial differential equations in recent decades. In this paper, we will discuss the asymptotic states of the solutions of the three-dimensional micropolar flow equation with nonlinear damping, especially the existence of uniform attractors of the solutions, and explore the continuous dependence of the solutions on some coefficients. The main research contents are as follows.

We study the existence of uniform attractors for 3D micropolar equation with nonlinear damping term. When3<β<5  , initial data(u_τ,ω_τ)∈V₁xV₂  and the external forces (f₁,f₂)∈ℋ(f₁⁰)xℋ(f₂⁰) , we give a series of uniform estimates on the solutions. According to these estimates, we prove the family of processes {U(f₁,f₂)(t,τ)}_t≥τ is((V₁xV₂)x(ℋ(f₁⁰)xℋ(f₂⁰)),V₁xV₂)  -continuous. Meanwhile, we find that {U(f₁,f₂)(t,τ)}t≥τ is (V₁xV₂,^₂(Ω)x²(Ω)) -uniformly compact. Finally, we obtain the existence of (V₁xV₂,^₂(Ω)x^₂(Ω)) -uniform attractor and (V₁xV₂,^₂(Ω)x^₂(Ω)) -uniform attractor. And we prove the (V₁xV₂ ,V₁xV₂) -uniform attractor is actually the (V₁xV₂,^₂(Ω)x^₂(Ω)) -uniform attractor.

We discuss the continuous dependence of the solutions of the three-dimensional micropolar flow equations with nonlinear damping on some coefficients. Firstly, by the uniform estimation of the solution of the equation in the uniform attractor. Secondly, with the help of these estimates, the differential inequality satisfied by the norm of the difference in the solution of the equation is obtained by using the trilinear inequality, Gagliardo-Nirenber inequality and the Gronwall inequality. Finally, by solving the differential inequality, the continuous dependence of the solution of the micropolar flow equation on initial values and coefficients  ν,κ,γ  is obtained.