In this paper, we study the initial–boundary value problem for an alpha-model, which describes the motion of weakly concentrated aqueous polymer solutions. We consider the mathematical model with a rheological relation, satisfying the objectivity principle. On the base of the topological approximation approach for studying hydrodynamic problems, we prove the existence of weak solutions to the alpha-model. We also demonstrate that solutions to the alpha-model converge to the solution of the original model as the value of the parameter alpha tends to zero.

中文翻译：

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聚合物溶液运动的 Alpha 模型

在本文中，我们研究了 alpha 模型的初始边界值问题，该模型描述了弱浓度聚合物水溶液的运动。我们考虑具有流变关系的数学模型，满足客观性原则。在研究流体动力学问题的拓扑近似方法的基础上，我们证明了α模型的弱解的存在。我们还证明了 alpha 模型的解收敛到原始模型的解，因为参数 alpha 的值趋于零。