Uniform attractors for non-autonomous motion equations of viscoelastic medium

Sufficient conditions for existence of minimal uniform trajectory attractors and uniform global attractors of non-autonomous evolution equations in Banach spaces are obtained. It is not assumed that the symbol space of an equation is a compact metric space and that the family of trajectory spaces corresponding to this symbol space is translation-coordinated or closed in any sense. Using these results, existence of minimal uniform trajectory attractors and uniform global attractors for weak solutions of the boundary value problem for motion equations of an incompressible viscoelastic medium with the Jeffreys constitutive law is shown. © 2006 Elsevier Inc. All rights reserved.