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In this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in H 4 ( Ω ) $H^{4}(\Omega )$ when the initial value belongs to H 1 ( Ω ) $H^{1}(\Omega )$ .

On global dynamics of 2D convective Cahn–Hilliard equation