  In recent literature several derivations of incompressible Navier-Stokes type
equations that model the dynamics of an evolving fluidic surface have been
presented. These derivations differ in the physical principles used in the
modeling approach and in the coordinate systems in which the resulting
equations are represented. This paper has overview character in the sense that
we put five different derivations of surface Navier-Stokes equations into one
framework. This then allows a systematic comparison of the resulting surface
Navier-Stokes equations and shows that some, but not all, of the resulting
models are the same. Furthermore, based on a natural splitting approach in
tangential and normal components of the velocity we show that all five
derivations that we consider yield the same tangential surface Navier-Stokes
equations.
