We first study the well-posedness of a non-autonomous incompressible non-Newtonian fluid with delay. The existence of global solution is obtained by classical Galerkin approximation and the energy method. Actually, we also prove the uniqueness of solution as well as the continuous dependence on the initial value. Then we analyze the long time behavior of the dynamical system associated to the incompressible non-Newtonian fluid. Finally, we establish the existence of pullback attractors for the non-autonomous dynamical system associated to the problem.

中文翻译：

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具有延迟的非自治不可压缩非牛顿流体动力学

我们首先研究具有延迟的非自主不可压缩非牛顿流体的适定性。全局解的存在性是通过经典伽辽金近似和能量方法获得的。实际上，我们也证明了解的唯一性以及对初始值的连续依赖。然后我们分析了与不可压缩的非牛顿流体相关的动力系统的长时间行为。最后，我们为与问题相关的非自治动力系统建立了回拉吸引子的存在。