Attractors for autonomous and nonautonomous 3D Navier-Stokes-Voight equations

Abstract

In this paper we study the long time behavior of the three dimensional Navier-Stokes-Voight model of viscoelastic incompressible fluid for the autonomous and nonautonomous cases. A useful decomposition method is introduced to overcome the difficulties in proving the asymptotical regularity of the 3D Navier-Stokes-Voight equations. For the autonomous case, we prove the existence of global attractor when the external forcing belongs to $V'.$ For the nonautonomous case, we only assume that $f(x,t)$ is translation bounded instead of translation compact, where $f=Pg$ and $P$ is the Helmholz-Leray orthogonal projection. By means of this useful decomposition methods, we prove the asymptotic regularity of solutions of 3D Navier-Stokes-Voight equations and also obtain the existence of the uniform attractor. Finally, we describe the structure of the uniform attractor and its regularity.