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We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy systemwhich is a diffuse-interface model for essentially immiscible two phaseincompressible flows with matched density in a karstic geometry. Existence offinite energy weak solution that is global in time is established in both 2Dand 3D. Weak-strong uniqueness property of the weak solutions is provided aswell.

Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry