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IGPM520.pdf March 2022 
TITLE 
Tangential NavierStockes equations on evolving surfaces: Analysis and simulations 
AUTHORS 
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov 
ABSTRACT 
The paper considers a system of equations that models a lateral flow of a BoussinesqScriven
fluid on a passively evolving surface embedded in R3. For the resulting NavierStokes type system, posed on
a smooth closed timedependent surface, we introduce a weak formulation in terms of functional spaces on
a spacetime manifold defined by the surface evolution. The weak formulation is shown to be wellposed for
any finite final time and without smallness conditions on data. We further extend an unfitted finite element
method, known as TraceFEM, to compute solutions to the fluid system. Convergence of the method is
demonstrated numerically. In another series of experiments we visualize lateral flows induced by smooth
deformations of a material surface 
KEYWORDS 
NavierStokes, surface partial differential equations, wellposedness, trace finite 