Global well-posedness of strong solutions to a bulk-surface Navier-Stokes-Cahn-Hilliard model with non-degenerate mobilities in two dimensions

We examine a thermodynamically consistent diffuse interface model for bulk-surface viscous fluid mixtures. This model consists of a Navier–Stokes–Cahn–Hilliard model in the bulk coupled to a surface Navier–Stokes–Cahn–Hilliard system on the boundary. In this paper, we address the global well-posedness of strong solutions in the two-dimensional setting, also covering the physically meaningful case of non-degenerate mobility functions. Lastly, we prove the uniqueness of the corresponding strong solutions and their continuous dependence on the initial data. Our approach hinges upon new well-posedness and regularity theory for a convective bulk-surface Cahn–Hilliard equation with non-degenerate mobilities, as well as a bulk-surface Stokes equation with non-constant coefficients.