在S^(2)局部坐标下的二维不可压Naiver-Stokes方程  

Two-dimensional incompressible Naiver-Stokes equations in local coordinates of S^(2)

作　　者：李小如 王术 耿范 LI Xiao-ru;WANG Shu;GENG Fan(School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2022年第1期53-58,共6页Journal of Guangzhou University:Natural Science Edition

摘　　要：考虑S^(2)局部坐标系下的二维不可压Naiver-Stokes方程的表达式及其在S^(2)_(+)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S^(2)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R^(2)中的能量守恒得到了在S^(2)_(+)中的能量等式。The expression of the two-dimensional incompressible Naiver-Stokes equation in the local coordinate system of S^(2) and the energy equation satisfied by the solution in the local coordinate system of S^(2)_(+)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 S^(2)_(+)is obtained by combining the energy conservation of the two-dimensional incompressible Naiver-Stokes equation in R^(2).

关 键 词：黎曼度量 S^(2) S^(2)_(+) 局部坐标 Naiver-Stokes方程 能量等式 

分 类 号：O351.1[理学—流体力学]