The unsteady Poiseuille flow of Carreau‐Yasuda fluid in a pipe, caused by a variable pressure gradient, is studied theoretically. As a special case, the steady flow is considered separately. It is proved that at some values of the viscosity model parameters, the problem has a generalized solution, while at others ‐ a classical solution. For the latter, a necessary and sufficient condition is found, which depends on the maximum pressure gradient and the Carreau‐Yasuda model parameters.

中文翻译：

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可变压力梯度下 Carreau-Yasuda 流体的泊肃叶流

从理论上研究了由可变压力梯度引起的卡罗-安田流体在管道中的非稳态泊肃叶流动。作为一种特殊情况，单独考虑稳定流。事实证明，在粘度模型参数的某些值下，问题具有广义解，而在其他值下，问题具有经典解。对于后者，找到了一个充分必要条件，该条件取决于最大压力梯度和 Carreau-Yasuda 模型参数。