二维Navier-Stokes方程的有限维性质

Finite Dimensionalities for the Planar Navier Stokes Equations

Ладыженская指出二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程具有如下的“有限维性质”：即由相空间中任一有界不变集出发的运动的决定模态个数有限，并且运动是周期的，如果它的决定模态具同一周期．

Ladyzhenskaya indicated in the planar Navier Stokes equations there exists a finite dimensionalities property as the following:the number of determining modes for any motion starting from a bounded invariant set in the phase space is finite,and this motion is periodic if its determining modes have same period. Ladyzhenskaya′s proof to the foregoing result is complemented and revised.