  We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy system
which is a diffuse-interface model for essentially 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.
