The Asymptotic Attractor And Boundary Layer Separation Of The Damped Navier-Stokes System

In this thesis,the asymptotic attractor and boundary layer separation for the two-dimensional damped Navier-Stokes system are studied.The main contents of this thesis are as follows.The first content is that the asymptotic attractor of two-dimensional damped Navier-Stokes system is obtained to construct finite-dimensional asymptotic solution sequence by orthogonal decomposition method.We proved that this solution sequence approximates the true solution infinitely after a long time.And the dimensional estimate of the asymptotic attractor is given.The second content is that solutions of the damped Navier-Stokes system is studied by using Taylor expansion of initial value and external force,which based on the geometry theory of incompressible fluid.The condition for vortex appearing in the process of fluid motion is obtained,and the time and place of boundary layer separation can be predicted by this condition.