Asymptotic Theory For The Damped Navier-Stokes Equations

The existence of the attractor in Hk space for any k?0 and decay of solutions in rectangular domains for the damped Navier-Stokes equations are investigated in this thesis.The main conclusion of this thesis consists of the following two parts.In part 1,we proved that the damped Navier-Stokes equations exists a global attractor A(?)Hk,which attracts all bounded set in the Hk-norm by using an iteration procedure and regularity estimates for the linear semigroup of operator,together with a classical existence theorem of global attractor.In part 2,the existence and uniqueness of global solutions on bounded rectangular domains for the damped Navier-Stokes equations is studied by energy methods.Solutions decay on rectangular domains in L2 space for the damped Navier-Stokes equations is obtained by the regularity estimates of elliptic equations.