二维不可压缩的Navier-Stokes方程四模类Lorenz方程组的稳定性分析

Analysis of Four-mode Truncation Lorenz Equations’Stability for Two-dimensional Incompressible Navier-Stokes Equations

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四模类Lorenz方程组,证明了此方程组吸引子的存在性,并对其稳定性进行了讨论和分析。

The plane incompressible Navier-Stokes equations was expanded in two dimensional square on a torus, then a four-modes truncation Lorenz equations were obtained. Further, the existence of attractor for the equations was also verified, with the stability of equations approached.