The Attractors For 2D-Navier-Stokes Equations With Delays

The attractors theory of Navier-Stokes Equations plays a great role in theory and applying when study turbulence and predict the 'future' behav-ior,also in industry such as ships manufacture and airplane design and etc. In this paper, we will study the existence of attractors of 2D-Navier-Stokes Equations with variable delays or distributed delays in smooth domains or in non-smooth domains, and intend to prove the existence of pullback attractors of the equations with Non-autonomous forces.In chapter 2, we will study the existence of global attractors for 2D-Navier-Stokes Equations with variable and distributed delays with non-homogeneous boundary condition. After transact the nonhomogeneous boundary conditions into homogeneous boundary conditions equivalently by using the Background flow functions,we get the existence of attractor in the phase space by the help of Ascoli-Arzela Theorem,In chapter 3, we will study the existence of global attractors for the equations with Non-homogeneous boundary conditions in non-smooth Lipshtiz domains. By using the Poincare inequality,Sobolev imbedding theorem, and energyinequality , the existence of global attractor is obtained.In chapter 4, we will study the existence of the pullback attractors of the non-autonomous 2D-Navier-Stokes Equations with delays. Because the lack of period or quasi-period condition, we will prove the existence of the attractors by using a general cocycle theory established by Kloeden etc. in their investigation of the random dynamical system.