Long-time Behavior Of Solutions Of 2D G-Navier-Stokes Equations With Delays On Unbounded Domains

The 2D non-autonomous g-Navier-Stokes equation has been found when Roh s-tudied the 3D non-autonomous Navier-Stokes equation on the thin domain in 2001,it is generalization of the 2D Navier-Stokes equation(i.e.,when g=1,it is the usual 2D Navier-Stokes equation).In recent years,Anh and Quyet have also investigat-ed the long-time behavior of the g-Navier-Stokes equation.In this master's thesis,exploiting the method of truncation function,combining with spatial domain decom-position technique,we consider the long-term behavior of the 2D non-autonomous g-Navier-Stokes equation with finite delay on the unbounded domain.Firstly,we recall some the research background and development of the 2D g-Navier-Stokes equa-tion;Secondly,the Galerkin approximation method is used to prove the existence and uniqueness of the weak solution of the non-autonomous 2D g-Navier-Stokes e-quation with finite delay on the unbounded domain;Finally,we show the existence of the pullback attractor of the equation on the unbounded domain.