N-S方程一般近似惯性流形构造和逼近

1．引言为了用有限维常微分方程来研究Navier七lobes（N七）方程的长时间动力学行为，Foias，Sell和Temaml］引入了耗散系统惯性流形的概念．但惯性流形存在的一个相当苛刻的条件一谱间隔条件一是包括N习方程在内的很多耗散系统无法满足的．因此，Foias，Manlea和TemamZ］随后又提出了近似惯性流形的概念．近似惯性流形也是一个光滑的Lipschitz流形，所有原方程的解在时间充分大时，将被吸引进入该流形的一个三邻域中．因其存在性不需要谱间隔条件来保证，从而可证明包括N－S方程在内的一大类耗散系统存在近似惯性流形．利用近似惯性…

CONSTRUCTION AND APPROXIMATION OF GENERAL APPROXIMATE INERTIAL MANIFOLDS FOR N-S EQUATIONS

In this paper, three general principles for constructing approximate inertial manifolds are provided, under which the associate approximate inertial form of origin problem, which is a finite dimensional ordinary differential equation, is well-possed and its solution will approximate the genuine solution at some degree. At last, for some kinds of approximate inertial manifolds and a family of approximate inertial manifolds, we indicate that the principles given here are suitable.