Uniform attractors of non-homogeneous micropolar fluid flows in non-smooth domains

Two-dimensional non-autonomous micropolar fluid flows in a Lipschitz bounded domain with non-homogeneous boundary conditions is investigated. For a normal external function, which is not necessarily translation compact, in L2loc (R; D(A-1/4)), the existence of a D(A1/4) uniform attractor abstracting bounded sets of L2 is shown. This attractor coincides with that derived by assuming the external function to be normal with respect to the weak topology of L2loc (R; D(A-1/4))