The Expression And Energy Of Navier-stokes Equations On S~2 Local Coordinate System

Firstly,we study Navier-Stokes equations in R~3and deduce the concrete for-m of Naiver-Stokes equations in ellipsoid coordinate system in three-dimensional Euclidean space,although the final equations form are somewhat complex.Sec-ondly,we extend the differential operators including gradient operator,divergence operator and Laplace operator of Euclidean space to manifolds,and derive the spe-cific expression of the Naiver-Stokes equations on the two-dimensional manifold S~2local coordinate system and the energy bounded on S_+~2.The content of this paper is arranged as follows:In Chapter 1,A brief introduction to the research background and some basic knowledge theories involved in presenting the main conclusions and basic concepts are introduced.In Chapter 2,The concrete form of Naiver-Stokes equations in ellipsoid co-ordinate system in three-dimensional Euclidean space are deduced based on some basic knowledge.The final equations form are somewhat complex,but also have certain research significance and value.In Chapter 3,The differential operators of Euclidean space are extended to manifolds,and the specific expression of the Naiver-Stokes equations on the two-dimensional manifold S~2local coordinate system and the energy boundedness on S_+~2are derived.