发展方程的时间离散化惯性流形－Ⅱ

TIME DISCRETIZATION INERTIAL MANIFOLDS FOR EVOLUTION EQUATION Ⅱ

“发展方程的时间离散化惯性流形－Ⅰ”中已经证明了如果时间步长充分小，且主算子Ａ满足谱间隔条件，则文中定义的一类耗散发展方程时间离散化的差分格式存在一个惯性流形Ｍｈ，它就是非线性映射Ｔ的不动点Φｈ∈Ｈｂ，ｌ的图象．第Ⅱ部分继而证明了当ｈ→０时，不动点Φｈ的收敛性．然后作为一个例子。

It has been proved that under some conditions there exists a fixed point Φ h for nonlinear inertial mapping T . Furthermore we obtained the graph of the Φ h which is an inertial manifold. In this paper the convergence of Φ h to Φ as h tends to zero is proved. Then as an example the theory is applied to the regularized Navier Stokes equations.