Asymptotic analysis of two-dimensional Oldroyd fluids in unbounded domains: Global attractors and their dimension

Article type: Research Article

Authors: Kinra, Kush^a | Mohan, Manil T.^{b; *}

Affiliations: [a] Tata Institute of Fundamental Research – Centre For Applicable Mathematics (TIFR-CAM), Bangalore 560065, Karnataka, India | [b] Department of Mathematics, Indian Institute of Technology Roorkee-IIT Roorkee, Haridwar Highway, Roorkee, Uttarakhand 247667, India

Correspondence: [*] Corresponding author. E-mails: maniltmohan@ma.iitr.ac.in, maniltmohan@gmail.com.

Abstract: In this work, we consider the two-dimensional Oldroyd model for the non-Newtonian fluid flows (viscoelastic fluid) in Poincaré domains (bounded or unbounded) and study their asymptotic behavior. We establish the existence of a global attractor in Poincaré domains using asymptotic compactness property. Since the high regularity of solutions is not easy to establish, we prove the asymptotic compactness of the solution operator by applying Kuratowski’s measure of noncompactness, which relies on uniform-tail estimates and the flattening property of the solution. Finally, the estimates for the Hausdorff as well as fractal dimensions of global attractors are also obtained.

Keywords: Oldroyd fluids, Global attractors, Kuratowski’s measure of noncompactness, uniform-tail estimates, flattening property, fractal and Hausdorff dimensions

DOI: 10.3233/ASY-241932

Journal: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-27, 2024