一个新平面不可压缩Navier-Stokes方程的五模类Lorenz方程组截断

New Five-mode Truncation of Navier-Stokes Equations for Two-dimensional Incompressible Fluid

对二维正方形区域上不可压缩的Navier-Stokes方程进行傅立叶展开后截断得到新五模类Lorenz方程组,证明了方程组吸引子的存在,并对其稳定性进行了讨论和证明,数值模拟了雷诺数变化时方程组的动力学行为。

Five-mode Lorenz equations were obtained after Fourier expansion and then truncation of the Navier-Stokes equations for a two dimensional incompressible fluid on a totus was done. The existence of attractor was proved. The stability of equations was discussed and proved. Numerical simulation of Reynolds numbers variation suggested there was a stochastic behavior exhibited by the equations.