A third-order highly non-linear ODE that arises in applications of non-Newtonian boundary-layer fluid flow, governed by a power-law Ostwald–de Waele rheology, is considered. The model appears in many disciplines related to applied and engineering mathematics, in addition to engineering and industrial applications. The aim is to use a new set of variables, defined via the first and second-order derivatives of the dependent variable, to transform the problem to a bounded domain, where we study properties of solutions, discuss existence and uniqueness of solutions, and investigate some physical parameter values and limitations leading to non-existence of solutions.

中文翻译：

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具有一阶和二阶导数非线性项的非牛顿流体边界层流动解的性质

考虑了在非牛顿边界层流体流动的应用中出现的三阶高度非线性 ODE，由幂律 Ostwald-de Waele 流变学控制。除了工程和工业应用之外，该模型还出现在与应用和工程数学相关的许多学科中。目的是使用一组通过因变量的一阶和二阶导数定义的新变量，将问题转换为一个有界域，在此我们研究解的性质，讨论解的存在性和唯一性，并调查一些物理参数值和限制导致解不存在。