This work provides a formulation of a fluid flow under a nonlinear diffusion based on a viscosity of Eyring–Powell type along with a degenerate semi-parabolic operator. The introduction of such a degenerate operator is significant as it allows us to explore a further general model not previously considered in the literature. Our aims are hence to provide analytical insights and numerical assessments to the mentioned flow model: firstly, some results are provided in connection with the regularity and uniqueness of weak solutions. The problem is converted into the travelling wave domain where solutions are obtained within an asymptotic expansion supported by the geometric perturbation theory. Finally, a numerical process is considered as the basis to ensure the validity of the analytical assessments presented. Such numerical process is performed for low Reynolds numbers given in classical porous media. As a main finding to highlight: we show that there exist exponential profiles of solutions for the velocity component. This result is not trivial for the non-linear viscosity terms considered.

中文翻译：

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使用简并算子深入了解 Eyring-Powell 流体流动模型：几何扰动


这项工作提供了基于艾林-鲍威尔型粘度和简并半抛物线算子的非线性扩散下流体流动的公式。这种简并算子的引入很重要，因为它使我们能够探索以前文献中未考虑过的进一步通用模型。因此，我们的目标是为上述流动模型提供分析见解和数值评估：首先，提供一些与弱解的规律性和唯一性相关的结果。该问题被转换为行波域，在几何微扰理论支持的渐近展开内获得解。最后，数值过程被认为是确保所提出的分析评估的有效性的基础。这种数值过程是针对经典多孔介质中给出的低雷诺数进行的。需要强调的一个主要发现是：我们证明速度分量的解存在指数分布。对于所考虑的非线性粘度项来说，这个结果并非微不足道。