Trajectory and Global Attractors of the Boundary Value Problem for Autonomous Motion Equations of Viscoelastic Medium

Abstract

We introduce the concept of minimal trajectory attractor generalizing the known concept of trajectory attractor of an abstract evolution equation. We obtain several results on existence and properties of minimal trajectory and global attractors without assumptions of any invariance of the trajectory space of an equation. With the help of these results we prove existence of minimal trajectory and global attractors for weak solutions of the boundary value problem for autonomous motion equations of an incompressible viscoelastic medium with the Jeffreys constitutive law.