This paper is concerned with the global existence and large time behavior of strong solutions to the Cauchy problem of one-dimensional compressible isentropic micropolar fluid model with density-dependent viscosity and microviscosity coefficients, where the far-fields of the initial data are prescribed to be different. The pressure $p\left(\rho \right)={\rho }^{\gamma }$ and the viscosity coefficient $\mathrm{\mu }\left(\rho \right)={\rho }^{\alpha }$ for some parameters $\alpha ,\gamma \in \mathbb{R}$ are considered. For the case when the corresponding Riemann problem of the resulting Euler equations admits two rarefaction waves solutions, it is shown that if the parameters $\alpha$ and $\gamma$ satisfy some conditions and the initial data is sufficiently regular, without vacuum and mass concentrations, then the Cauchy problem of the one-dimensional compressible micropolar fluid model has a unique global strong nonvacuum solution, which tends to a superposition of these two rarefaction waves as time goes to infinity. This result holds for arbitrarily large initial perturbation and large-amplitudes rarefaction waves. Moreover, the exponential time decay rate of the microrotation velocity $\omega (t,x)$ under large initial perturbation is also derived. The proof is given by an elaborate energy method and the key ingredient is to deduce the uniform-in-time lower and upper bounds on the specific volume.

本文关注一维可压缩等熵微极性流体模型的柯西问题的强解的整体存在和长时间行为，该柯西问题具有密度依赖的粘度和微粘度系数，其中规定了初始数据的远场是不同。压力$p（\rho ）={\rho }^{\gamma }$ 和粘度系数 $\mathrm{\mu }（\rho ）={\rho }^{\alpha }$ 对于某些参数 $\alpha ，\gamma \in \mathbb{[R}$被考虑。对于由此产生的欧拉方程的相应黎曼问题允许两个稀疏波解的情况，表明$\alpha$ 和 $\gamma$满足某些条件并且初始数据足够规则，没有真空和质量浓度，则一维可压缩微极性流体模型的柯西问题具有唯一的全局强非真空解，随着时间的推移，这倾向于将这两个稀疏波叠加去无穷大。该结果适用于任意大的初始扰动和大振幅的稀疏波。而且，微旋转速度的指数时间衰减率$\omega （Ť，X）$在较大的初始扰动下也可以得到。证明是通过精心设计的能量方法给出的，关键要素是推导出特定体积上时间上一致的下限和上限。