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We will present our recent results on a Cahn-Hilliard-Stokes-Darcy system which is a diffuse-interface model for immiscible two phase incompressible flows with matched density in a karstic geometry.Existence of finite energy weak solution that is global in time is established in both 2D and 3D.Weak-strong uniqueness property of the weak solutions is provided as well.This is a joint work with Prof.Xiaoming Wang and Dr.Daozhi Han.