Abstract:

\noindent{\bf Abstract:} In this paper, the authors propose the concept of stream surface and stream layer. By using classical tensor calculus, the authors derive 3D Navier-Stokes Equations(NSE) in the stream layer under
semigeodesic coordinate system, Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface, a nonlinear initial-boundary value problem satisfied by stream function is obtained,existence and uniqueness of its solution are proved. Based on this theory the authors propose a new method called ``dimension split method" to solve 3D NSE.

Key words: Stream Layer, Stream surface, Dimension Split Method, Navier-Stokes equations