地磁流体方程的近似惯性流形的逐次逼近求解

Solving Approximate Inertial Manifolds Equations for the Flow and Magnetic Field within the Earth by Successive Approximation Method

证明了地磁流体方程非线性项在给定区域的有界性,利用逐次逼近方法构造了二维地磁流体方程的几种不同形式的近似惯性流形,并证明了该方程的任意解轨道在长时间后进入近似惯性流形的任意小邻域中.

In this paper,the boundness of nonlinear term in the equations for the flow and magnetic field within the earth is proved in a given region. Several different kinds of apprixomate inertial manifolds in the twodimensional case are constructed by successive approximation method and it is proved that arbitrary trajectory of such equation enters into a small neighbourhood of such manifold after long time.