For the non-isentropic compressible micropolar fluids in three dimensions, we show that the space–time behaviors of the fluid density, momentum and energy contain both generalized Huygens’ wave and diffusion wave as the non-isentropic compressible Navier–Stokes equation, while it only contains the diffusion wave for the micro-rational velocity. All of the previous estimates containing Huygens’ waves for wave behaviors of compressible flow models rely heavily on the conservative structure, for instance, the isentropic and non-isentropic Navier–Stokes equations. In this paper, after using the decomposition of fluid and electromagnetic parts to study three smaller Green’s matrices, we find that one of them is like a non-isentropic Navier–Stokes equation, but its energy is not conservative anymore due to the presence of the micro-rational velocity. We overcome this difficulty by providing a refined estimate for this Green’s matrix. Another difficulty is in proving the pointwise estimate of the micro-rational velocity only contains the diffusion wave, although its nonlinear terms contain both the Huygens’ wave and the diffusion wave. It is solved by using the relation of these two waves and developing new nonlinear estimates. Our pointwise estimate directly yields \(L^p\)-estimate with \(p>1\), which is a generalization of the usual \(L^2\)-estimate.

对于三维的非等熵可压缩微极性流体，我们表明，流体密度，动量和能量的时空行为既包含广义惠更斯波，也包含扩散波，作为非等熵可压缩Navier–Stokes方程，仅包含微理性速度的扩散波。包含惠更斯波的可压缩流模型的所有先前估计都严重依赖于保守结构，例如，等熵和非等熵Navier-Stokes方程。在本文中，使用流体和电磁部分的分解研究了三个较小的格林矩阵，我们发现其中一个类似于非等熵的Navier–Stokes方程，但是由于存在该方程，其能量不再是保守的微理性速度。我们通过提供此格林矩阵的精确估计值来克服此困难。另一个困难是要证明微理性速度的逐点估计仅包含扩散波，尽管其非线性项既包含惠更斯波也包含扩散波。通过使用这两个波的关系并开发新的非线性估计来解决该问题。我们的逐点估计直接产生\（L ^ p \）-用\（p> 1 \）估计，这是通常的\（L ^ 2 \）-估计的推广。