考虑Ｓ２局部坐标系下的二维不可压Ｎａｉｖｅｒ-Ｓｔｏｋｅｓ方程的表达式及其在Ｓ２局部坐标系下解满足的能＋量等式。利用黎曼度量，结合流形上的几个微分算子，推导在Ｓ２局部坐标下的Ｎａｉｖｅｒ-Ｓｔｏｋｅｓ方程的具体表达式，并结合二维不可压Ｎａｉｖｅｒ-Ｓｔｏｋｅｓ方程在Ｒ２中的能量守恒得到了在Ｓ２中的能量等式。＋

The expression of the two dimensional incompressible Naiver Stokes equation in the local coordinate system of S2 and the energy equation satisfied by the solution in the local coordinate system of S2 are considered. By using the Riemannian metric and combining several differential operators on the manifold, the specific expression of the Naiver Stokes equation in the local coordinate system is derived, and the energy equation on S2 is obtained by combining the energy conservation of the two dimensional incompressible Naiver Stokes equation in R2 .