Affiliations: [a] College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046, P.R. China | [b] Department of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, P.R. China | [c] Laboratoire de Mathématiques et Applications, Université de Poitiers, Site du Futuroscope-Téléport 2, 11 Boulevard Marie et Pierre Curie, Bâtiment H3, TSA 61125, 86073 Poitiers Cedex 9, France | [d] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, P.R. China
Abstract: This paper is concerned with the dynamics of the two-dimensional Navier–Stokes equations with multi-delays in a Lipschitz-like domain, subject to inhomogeneous Dirichlet boundary conditions. The regularity of global solutions and of pullback attractors, based on tempered universes, is established, extending the results of Yang, Wang, Yan and Miranville (Discrete Contin. Dyn. Syst. 41 (2021) 3343–3366). Furthermore, the robustness of pullback attractors when the delays, considered as small perturbations, disappear is also derived. The key technique in the proofs is the application of a retarded Gronwall inequality and a variable index for the tempered pullback dynamics, allowing to obtain uniform estimates and the compactness of the process.
