The Attractors Of Two Nonlinear Evolution Equations

In this passage, we discussed some problems related to attractors of Infinite Dimensional Dynamical Systems and introduced development trends about Infinite Dimensional Dynamical Systems in recent decades. Particularly, we considered partly reaction diffusion equation in unbounded domain. In2000 years, Bernal and Wang[17] acquired the existence about global attractors of partly dissipative reaction diffusion equation in unbounded domain of Hilbert space L2 ( R n )×L2 ( Rn).In their consequences, the coefficient of reaction term is constant, however, this passage deals with more general cases and the coefficient of reaction term depends on the space varieties.We got the existence about global attractors through the estimation of solutions and operator decomposition which used standard consequence of literature [1].In addition, we considered the long behavior of the solution of 2D Navier-Stokes equation ut ?γ?u + ( u ?? ) u +? p= f ( x ), ? ? u =0, and obtained the existence of asymptotic attractors based on the existence of globle attractors and AIM of this equation and gave the dimension estimation of asymptotic attractors.