Global Attractors and Determining Functionals for Helical Flows of Maxwell Fluid

Abstract

This paper is dedicated to the long-time behavior of a system of coupled one-dimensional wave equations modeling helicoidal flows of Maxwell fluid. In a scenario featuring nonlinear damping and source terms of arbitrary polynomial growth, we prove the existence of smooth finite dimensional global attractors as well as exponential attractors. We also prove that its long-time dynamics is completely determined by a finite set of linear continuous functionals.