流面上的Navier-Stokes方程及其维数分裂方法

该文首先提出了流面和流层的概念,然后推导出了半测地坐标系下流层内的三维NS (Navier-Stokes)方程,以及流面上的二维NS方程.通过引入流面上的流函数,得到了流函数方程的非线性初边值问题,并讨论了方程解的存在性和唯一性.基于以上讨论,提出了求解三维NS方程的维数分裂方法, 并给出了算例.

The Navier-Stokes Equations in Stream Layer or on Stream Surface and a Dimension Split Method

\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 undersemigeodesic 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.