PULLBACK ATTRACTOR FOR A CLASS OF NON-AUTONOMOUS FUNCTIONAL HYDRODYNAMICAL TYPE EQUATIONS

Abstract

This research investigates a specific class of non-autonomous functional hydrodynamical type equations. The focus lies on establishing the existence of a pullback attractor for this system. Pullback attractors are a mathematical concept used to describe the long-term behavior of dynamical systems. In this context, the pullback attractor represents a set that attracts all solutions of the equation as time progresses. By proving the existence of a pullback attractor, the study demonstrates that solutions to these non-autonomous hydrodynamical equations eventually converge to a specific set over time, regardless of their initial conditions. This finding provides valuable insights into the long-term dynamics of the system, which can be helpful in understanding and predicting the behavior of fluid flows governed by such equations.