In 2018, Duan [1] studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model. Due to the absence of heat conductivity, it is quite difficult to close the energy estimates. He considered the far-field states of the initial data to be constants; that is, $$\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = (1,0,0,1)$$ . He proved that the solution tends asymptotically to those constants. In this article, under the same hypothesis that the heat conductivity is zero, we consider the far-field states of the initial data to be different constants — that is, $$\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = ({v_ \pm },{u_ \pm },0,{\theta _ \pm })$$ -and we prove that if both the initial perturbation and the strength of the rarefaction waves are assumed to be suitably small, the Cauchy problem admits a unique global solution that tends time — asymptotically toward the combination of two rarefaction waves from different families.

中文翻译：

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零热导率可压缩微极流体模型稀薄波的非线性稳定性

2018年段[1]对一维可压缩微极流体模型热导率为零的情况进行了研究。由于不存在热导率，因此很难接近能量估计值。他认为初始数据的远场状态是常数；即 $$\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = (1, 0,0,1)$$。他证明了该解决方案渐近地趋向于这些常数。在本文中，在导热系数为零的相同假设下，我们将初始数据的远场状态视为不同的常数——即 $$\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = ({v_ \pm },{u_ \pm },0,