Inertial Manifolds For The 3D Hyperviscous Navier-stokes Equation With L~2 Force

This dissertation devotes to the finite dimensional reduction for the hyperviscous Navier-Stokes equation and prove the existence of an -dimensional inertial manifold for this problem.Employing the asymptotic regularity method,for the problem with lower regular external force,we first prove the existence of a regular global attractor,and construct an -dimensional inertial manifold for the ’prepared’ equation via the so-called spatial averaging methods;then,we clarify further that the inertial manifold of the ’prepared’ equation is also an inertial manifold of the original problem.