The Research On The Long-term Behavior Of Solutions To Two Kinds Of Nonlinear Evolution Equations

In this dissertation,the exponential attractor of the 2D Navier-Stokes equation with damping term and the viscous Cahn-Hilliard equation are investigated,and the upper semi-continuity of pullback attractors for 3D Navier-Stokes equation with damping term is discussed.Firstly,the exponential attractor of the 2D Navier-Stokes equation with damping terms on a bounded domain is studied in this dissertation.There are weak and strong solutions to the equation respectively when the damping termau~buisb30 and1/3?b?2,the existence of bounded absorbing set and satisfying condition C of solution semigroups are verified,thus the existence of the exponential attractor of the 2D Navier-tokes equation with damping term is obtained.Secondly,it is discussed that the solution semigroup corresponding to the viscous Cahn-Hilliard equation is Lipschitz continuous and has Squeezing property in the space of V,the existence of exponential attractor in the equation in space of V is proved.Finally,the semi-continuity of pullback attractors for 3D Navier-Stokes equation with damping under external forces perturbation is proved.The existence of global attractors for autonomous systems is achieved by using the decomposition method of semigroups and the weak continuous method.Furthermore,whene(29)0 converges toe(28)0,pullback attractors for nonautonomous systems can converge continuously to global attractors for autonomous systems.