Shen Hui-chuan. Exact Solution of Navier-Stokes Equations——The Theory of Functions of a Complex Variable under Dirac- Pauli Representation and Its Application in Fluid Dynamics (Ⅱ)[J]. Applied Mathematics and Mechanics, 1986, 7(6): 517-522.
 Citation: Shen Hui-chuan. Exact Solution of Navier-Stokes Equations——The Theory of Functions of a Complex Variable under Dirac- Pauli Representation and Its Application in Fluid Dynamics (Ⅱ)[J]. Applied Mathematics and Mechanics, 1986, 7(6): 517-522.

# Exact Solution of Navier-Stokes Equations——The Theory of Functions of a Complex Variable under Dirac- Pauli Representation and Its Application in Fluid Dynamics (Ⅱ)

• Publish Date: 1986-06-15
• This work is the continuation of the discussion of Ref. [1]. In Ref. [1] we applied the theory of functions of a complex variable under Dirac-Pauli representation, introduced the Kaluza "Ghost" coordinate, and turned Navier-Stokes equations ofviscofluid dynamics of homogeneous and incompressible fluid into nonlinear, equation with only a pair of complex unknown functions. In this paper we again combine the complex independent variable except time, and caust it to decrease in a pair to the number of complex independent variables. Lastly, we turn Navier-Stokes equations into classical Burgers equation. The Cole-Hopf transformation join up with Burgers equation and the diffusion equation is Backlund transformation in fact, and the diffusion equation has the general solution as everyone knows. Thus, we obtain the exact solution of Navier-Stokes equations by Backlund transformation.
•  [1] 沈惠川,Dirac-Pauli表象的复变函数理论及其在流体力学的应用(I),应用数学和力学,1. 4(1986). [2] Lapedes, D,N,,科学技术百科全书》,1.《数学,四元数》,科学出版社(1980).252. [3] Eddiagton, A, S,,Fundamental Theorg, Cambr, Univ, Press, London (1953). [4] Dirac,P,A,M,,《量子力学原理》,陈咸亨译,科学出版社(1965). [5] Flügge, S,《实用量子力学》,宋孝同等译,人民教育出版社(1981-1983). [6] Lapedes, D,N,《科学技术百科全书》,2. 《力学,凯莱一克莱因参量》,科学出版社(1982),116. [7] Klein, F,,Elementarb Mathematics from an Advanced Standpoint; Arithmetic, Algebra,Analgsis, Tr, from the 3rd German ed, by E.R, Hedrick aad A.Noble,Dover, n,d.,N.Y. (1924). [8] Бранеп В.Н.и И.П.Шмыглевский,《K四元数在刚体定位问题中的应用》,梁振和译,国防工业出版社(1977). [9] Fung, Y, C,(冯元祯),《连续介质力学导论》,李松年、马和中译,科学出版社(1984). [10] Ландау Л.Д.и Е.М.Лифшип,《连续介质力学》,彭旭麟译,人民教育出版社(1958).Ландау Л.Д.и Е.М.Лифшип《流体力学》,孔祥言、徐燕侯、庄礼贤译,高等教育出版社(1.983-1984). [11] 渴川秀榭,《现代物理学の基础》,(第一版)1,《古典物理学扮,岩波书店(1975). [12] Prandtl, L,, K, Oswatitsch and K, Wieghardt,《流体力学概论》,郭永怀、陆士嘉译,科学出版社(1981). [13] Oswatitsch, K,, K气体动力学》,徐华舫译,科学出版社(1965). [14] Lightill, M J,,Survegs in Mechanics, Cambr, Univ, Press, London (1956). [15] 谷内俊弥、西原功修,《非线性波动》,徐福元等译,原子能出版社(1981). [16] Eckhans, W, and A, Yan Harten,《逆散射变换和孤立子理论》,黄迅成译,陈以鸿校,上海科学技术文献出版社(1984). [17] 沈惠川,均匀不可压缩蠕流动力学的通解,自然杂志,7,10(1984), 799; 7,12(1984), 940.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142