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IGPM518.pdf October 2021 
TITLE 
On derivations of evolving surface NavierStokes equations 
AUTHORS 
Philip Brandner, Arnold Reusken, Paul Schwering 
ABSTRACT 
In recent literature several derivations of incompressible NavierStokes 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 NavierStokes equations into one framework. This then allows
a systematic comparison of the resulting surface NavierStokes 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 NavierStokes equations. 
KEYWORDS 
surface PDEs, NavierStokes on surfaces 