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A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures

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  • An initial-boundary-value problem for the sixth order Cahn-Hilliard type equation in 3-D is studied. The problem describes phase transition dynamics in ternary oil-water-surfactant systems. It is based on the Landau-Ginzburg theory proposed for such systems by G. Gompper et al. We prove that the problem under consideration is well posed in the sense that it admits a unique global smooth solution which depends continuously on the initial datum.
    Mathematics Subject Classification: Primary: 35K50, 35K60; Secondary: 35Q72, 35L205.


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