Attractors For Evolution Equations With Finite Delay

In this paper,we study the existence of attractors for evolution equations with finite delay.Firstly,we study the existence of global attractor for a Semi-linear Evolution Equa-tion with finite delay.When the external force f satisfies the linear growth condition,by using the fixed point theorem of Banach,the unique mild solution is obtained.The compactness of the system corresponding to the semigroup is obtained by using the Arzela-Ascoli Theorem.And then the existence of the global attractor is verified by the two additional inequalities.The two inequalities make the condition of the verification more relaxed,and thus the time delay interval of the system is enlarged.Nextly,we study the existence of uniform attractors for Navier-Stokes equations with finite delay.Where ? is the area in Rn,and(?)? is its boundary.When the non-autonomous external force term f satisfies the translational,bounded and normal conditions.And the external force term g with time delay satisfies the measurability and other conditions at the same time.The bounded absorbing set of the system in the corresponding space is obtained by constructing new mapping.Finally,the existence of the uniform attractor is obtained by using the classical spectral theory and the estimation of the related inequalities.