Tangential Navier–Stokes equations on evolving surfaces: Analysis and simulations

The paper considers a system of equations that models lateral flow Boussinesq–Scriven fluid on passively evolving surface embedded in [Formula: see text]. For the resulting Navier–Stokes type system, posed smooth closed time-dependent surface, we introduce weak formulation terms functional spaces space-time manifold defined by evolution. is shown to be well-posed for any finite final time and without smallness conditions data. We further extend an unfitted element method, known as TraceFEM, compute solutions system. Convergence method demonstrated numerically. In another series experiments visualize flows induced deformations material surface.