Dynamics of non-autonomous equations of non-Newtonian fluid on 2D unbounded domains
Caidi Zhao · Dynamics of Partial Differential Equations · 2013
This paper studies the asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid on two-dimensional unbounded domains.We first prove the existences of the L 2 -regularity uniform attractors A H H(g 0 ) and H 2 -regularity uniform attractor A V H(g 0 ) , respectively.Then we establish the regularity of the uniform attractors by showing, which implies the uniform (with respect to the external forces) asymptotic smoothing effect of the non-autonomous fluid in the sense that the solutions become eventually more regular than the initial data.