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On weak solutions to a diffuse interface model of a binary mixture of compressible fluids

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  • We consider the Euler-Cahn-Hilliard system proposed by Lowengrub and Truskinovsky describing the motion of a binary mixture of compressible fluids. We show that the associated initial-value problem possesses infinitely many global-in-time weak solutions for any finite energy initial data. A modification of the method of convex integration is used to prove the result.
    Mathematics Subject Classification: Primary: 35A01; Secondary: 35Q31, 35Q35.

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