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Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry. (English) Zbl 1302.35217
Summary: 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.

##### MSC:
 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 76S05 Flows in porous media; filtration; seepage 76D07 Stokes and related (Oseen, etc.) flows 35Q35 PDEs in connection with fluid mechanics 35D30 Weak solutions to PDEs
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