关键词: micropolar fluids, rarefaction wave, zero-heat conductivity

Abstract: 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, $\lim\limits_{x\rightarrow \pm\infty}(v_0,u_0,\omega_0,\theta_0)(x)=(1,0,0,1)$. 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, $\lim\limits_{x\rightarrow \pm\infty}(v_0,u_0,\omega_0,\theta_0)(x)=(v_\pm, u_\pm, 0, \theta_\pm)$-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.

Key words: micropolar fluids, rarefaction wave, zero-heat conductivity