Pullback Attractors For 2D Navier-Stokes Equations On Time-Varying Domains

In this master paper, we investigate the dynamic behavior of two dimensional Navier-Stokes equations on time-varying domains in the case of diffeomorphism,Firstly, we prove the existence and uniqueness of the weak solution of the vari-able regional problem by the coordinate transformation and Faedo-Galerkin approxima-tion. Secondly, we establish priori estimates of the weak solution in L2(τ,T; Vt) and L∞(τ,T; Ht) to prove the existence of the family of Dλ1-pullback absorbing sets for the system. Finally, in order to overcome the difficulties from regional change, we prove that the solution process is Dλ1-pullback asymptotically compact by using the method of finite ε-net, hence, we obtain the existence of Dλ1-pullback attractors of 2D Navier-Stokes equations on time-varying domains.