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Micropolar fluid flows with delay on 2D unbounded domains
Keywords:Micropolar fluid flow, Truncation function, Well-posedness, Exponential stability.
      In this paper, we investigate the incompressible micropolar fluid flows on 2D unbounded domains with external force containing some hereditary characteristics. Since Sobolev embeddings are not compact on unbounded domains, first, we investigate the existence and uniqueness of the stationary solution, and further verify its exponential stability under appropriate conditions – essentially the viscosity δ_1 := min{ν,c_a +c_d } is asked to be large enough. Then, we establish the global well-posedness of the weak solutions via the Galerkin method combined with the technique of truncation functions and decomposition of spatial domain.