We consider a mathematical model with delay for non-Newtonian incompressible fluids in a bounded domain. Existence of global weak solutions is proved under suitable regularity on the initial data and the forces. Conditions for uniqueness are also given, but in general the results are stated in a multi-valued framework. Suitable multi-valued dynamical systems are well-posed, using basically or norms. Then the existence of pullback attractors is ensured acting on several universes, some of them of fixed bounded sets and others of tempered type, depending on parameters related to an integrability condition of the force and the delay term. Finally, relationships between these families of attractors are also provided, improving the characterization of attraction with respect to previous results.

中文翻译：

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具有非线性剪切张量和遗传条件的非牛顿不可压缩流体


我们考虑有界域中非牛顿不可压缩流体的延迟数学模型。在初始数据和力的适当规律下证明了全局弱解的存在性。还给出了唯一性的条件，但一般来说结果是在多值框架中陈述的。合适的多值动力系统是适定的，使用基本或规范。然后，根据与力和延迟项的可积条件相关的参数，确保回拉吸引子的存在作用于多个宇宙，其中一些是固定有界集，另一些是调和类型。最后，还提供了这些吸引子家族之间的关系，从而相对于之前的结果改进了吸引力的表征。