On the Dynamics of a Viscoelastic Fluid with Memory

The existence of a weak solution to a boundary value problem for a high-order Oldroyd-type viscoelastic fluid model with memory along the trajectories of the velocity field over an infinite time interval is established. In the paper, we use the solvability of the corresponding approximation initial–boundary value problem over a finite time interval and subsequently pass to the limit over an infinite time interval.