The goal of this paper is to derive governing equations for complex fluids in a thermodynamically consistent way so that the conservation of energy and the increase of entropy is guaranteed. The model is a system of first-order partial differential equations on density, velocity, energy (or equivalently temperature), and conformation tensor. A barotropic model is also derived. In the one-dimensional case, we express the barotropic model in the form of hyperbolic balance laws, and show that it satisfies the stability condition. Consequently, the global existence of solutions around equilibrium states is proved and the convergence rates is obtained.

中文翻译：

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复杂流体和数学分析的热力学一致建模

本文的目标是以热力学一致的方式推导复杂流体的控制方程，从而保证能量守恒和熵的增加。该模型是关于密度、速度、能量（或等效温度）和构象张量的一阶偏微分方程系统。还导出了正压模型。在一维情况下，正压模型以双曲线平衡定律的形式表达，并证明其满足稳定性条件。因此，证明了平衡状态周围解的全局存在性并获得了收敛速度。