Navier-Stokes方程的精确解——Dirac-Pauli表象的复变函数理论及其在流体力学中的应用(Ⅱ)
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)
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摘要: 本文是文[1]的继续。在文[1]中我们应用Dirac-Pauli表象的复变函数理论并引入Kaluza“鬼”坐标,将不可压缩粘流动力学的Navier-Stokes方程化成只有一对复未知函数的非线性方程。在本文中,我们将除时间之外的复自变量进行重新组合,从而成对地减少了复自变量的数目。最后,我们将Navier-Stokes方程化成经典的Burgers方程。联结Burgers方程与扩散方程的Cole-Hopf变换实际上是Bäcklund变换,而扩散方程众所周知是具有通解的。于是,我们利用Bäcklund变换求得了Navier-Stokes方程的精确解。Abstract: 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.
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