Abstract: In this paper, we study the well-poseness of a non-autonomous delayed incompressible non-Newtonian fluid on 2D unbounded domains. With a minimal regularity of the force, we prove the existence f solutions by the method of combining the technique of domain decomposition with the Garlerin approximation. Then we use the energy method to prove the uniqueness and the stability of solutions.

Key words: Non-Newtonian fluid, Delay, Well-posedness.