| Abstract: |
| We present a new diffuse interface model for incompressible, viscous fluid mixtures with bulk-surface interaction. This system consists of a Navier--Stokes--Cahn--Hilliard model in the bulk that is coupled to a surface Navier--Stokes--Cahn--Hilliard model on the boundary. Compared with previous models in the literature, the inclusion of an additional surface Navier--Stokes equation is motivated, for example, by biological applications. We prove the existence of weak solutions by means of a semi-Galerkin scheme combined with a fixed-point argument. To discretize the Navier--Stokes subsystem, we analyze a novel bulk-surface Stokes system and its corresponding bulk-surface Stokes operator, whose eigenfunctions serve as a natural basis to approximate the velocity fields.
This is joint work with Patrik Knopf (University of Regensburg) |
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