Abstract We are concerned with the large-time behavior of the Cauchy problem to the 3d micropolar fluids in an infinite long flat nozzle domain R × T 2 . In one dimensional case, this system tends time-asymptotically to the Navier–Stokes equations. That is to say, the basic wave patterns to the compressible micropolar fluids model are stable. Hence, in this paper we consider the nonlinear stability of planar rarefaction wave to the corresponding three dimensional model. Some cancellations on the flux terms and viscous terms are crucial. Moreover, a proper combining of damping term and rotation terms can provide an extra regularity of w.

中文翻译：

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平面稀疏波对 3D 微极方程的渐近稳定性

摘要 我们关注柯西问题对无限长扁平喷嘴域 R × T 2 中 3d 微极流体的长时间行为。在一维情况下，该系统时间渐近地趋向于 Navier-Stokes 方程。也就是说，可压缩微极流体模型的基本波型是稳定的。因此，在本文中，我们考虑平面稀疏波对相应三维模型的非线性稳定性。对通量项和粘性项的一些抵消是至关重要的。此外，阻尼项和旋转项的适当组合可以提供 w 的额外规律。